{"id":11522,"date":"2021-10-15T11:42:20","date_gmt":"2021-10-15T08:12:20","guid":{"rendered":"https:\/\/cfd-mrk.ir\/?page_id=11522"},"modified":"2021-11-28T09:15:11","modified_gmt":"2021-11-28T05:45:11","slug":"solving-hyperbolic-pdes-using-fdm","status":"publish","type":"page","link":"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/solving-hyperbolic-pdes-using-fdm\/","title":{"rendered":"\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f"},"content":{"rendered":"

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/span><\/h2>\n

Solving Hyperbolic PDEs Using FDM<\/strong><\/span><\/h2>\n

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u062f\u0631 \u0627\u06cc\u0646 \u067e\u0633\u062a \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0639\u0631\u0648\u0641\u200c\u062a\u0631\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u0647 \u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f. \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u062d\u0644 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062a\u0646\u0648\u0639 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0645\u0639\u0627\u062f\u0644\u0647 (1) \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u0627\u0633\u062a. \u0645\u0639\u0627\u062f\u0644\u0647 (2) \u0646\u06cc\u0632 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a<\/p>\n

\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u06af\u0648\u0646\u0627\u06af\u0648\u0646\u06cc \u0628\u0631\u0627\u06cc \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0637\u0631\u062d \u0634\u062f\u0647 \u06a9\u0647 \u062f\u0631 \u0642\u0627\u0644\u0628 \u062f\u0648 \u0646\u0648\u0639 \u0635\u0631\u06cc\u062d \u0648 \u0636\u0645\u0646\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0627\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627 [1] \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 (\u0645\u0639\u0627\u062f\u0644\u0647 1) \u062f\u0631 \u0642\u0627\u0644\u0628 \u0645\u062b\u0627\u0644 (1) \u0648 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u0628\u0635\u0648\u0631\u062a \u0645\u062b\u0627\u0644 (2) \u0628\u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u062a\u0634\u0631\u06cc\u062d \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

<\/a>\u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0627 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/span><\/strong><\/span><\/h2>\n

\u0628\u0639\u0646\u0648\u0627\u0646 \u0627\u0648\u0644\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f (\u0645\u062b\u0627\u0644-1). \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u00a0\u0633\u0631\u0639\u062a \u0635\u0648\u062a (300 \u0645\u062a\u0631 \u0628\u0631 \u062b\u0627\u0646\u06cc\u0647) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0627\u063a\u062a\u0634\u0627\u0634\u06cc \u062f\u0631 \u062f\u0627\u062e\u0644 \u06cc\u06a9 \u0644\u0648\u0644\u0647 \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u06a9\u0647 \u0647\u0631 \u062f\u0648 \u0627\u0646\u062a\u0647\u0627\u06cc \u0622\u0646 \u0628\u0633\u062a\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u0627\u0639\u0645\u0627\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0627\u063a\u062a\u0634\u0627\u0634 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0 \u0628\u0647 \u0634\u06a9\u0644 \u06cc\u06a9 \u0645\u0648\u062c \u0633\u06cc\u0646\u0648\u0633\u06cc \u0628\u0627 \u0634\u0631\u0627\u0626\u0637 \u0627\u0648\u0644\u06cc\u0647 \u0632\u06cc\u0631 \u0627\u0639\u0645\u0627\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/span><\/p>\n

\"\u0645\u062b\u0627\u0644-1<\/p>\n

\u0647\u062f\u0641 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0641\u0648\u0642 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0639\u062f\u062f\u06cc \u0648 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0622\u0646 \u0628\u0627 \u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc (\u062f\u0642\u06cc\u0642)<\/a> <\/span><\/strong>\u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644<\/strong><\/span><\/span><\/h3>\n

\u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u062a\u0639\u062f\u062f\u06cc \u0628\u0631\u0627\u06cc \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0635\u0631\u06cc\u062d \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 (\u0645\u0639\u0627\u062f\u0644\u0647 2) \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0634\u062f\u0647 \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0642\u0633\u0645\u062a \u0628\u0647 \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u0644\u0632\u0627\u0645\u0627\u064b \u062a\u0645\u0627\u0645\u06cc \u0631\u0648\u0634\u0647\u0627\u06cc \u0628\u06cc\u0627\u0646 \u0634\u062f\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0646\u06cc\u0633\u062a \u0648 \u0628\u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627 \u0646\u06cc\u0632 \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0648 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u067e\u06cc\u0634 \u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u067e\u0633\u0631\u0648 \u062f\u0631 \u0645\u06a9\u0627\u0646 (Forward in Time and Backward in Space: FTBS)<\/strong><\/span><\/span><\/h4>\n

\u062f\u0631 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0628\u0627\u0644\u0627\u062f\u0633\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (2) \u0628\u0635\u0648\u0631\u062a \u067e\u06cc\u0634 \u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u067e\u0633\u0631\u0648\u00a0\u062f\u0631 \u0645\u06a9\u0627\u0646 \u06af\u0633\u0633\u062a\u0647 \u0633\u0627\u0632\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0641\u0631\u0645 \u06af\u0633\u0633\u062a\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (3) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0647 \u062f\u0642\u062a \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 \u06cc\u06a9 (\u0394x<\/em><\/strong>) \u0627\u0633\u062a. <\/span>\u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0631\u0648\u0634 \u06cc\u0627\u062f \u0634\u062f\u0647 \u06cc\u06a9 \u0631\u0648\u0634 \u0635\u0631\u06cc\u062d \u0627\u0633\u062a\u060c \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0644\u0627\u0632\u0645 \u0627\u0633\u062a \u06a9\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0631\u0633\u06cc \u0634\u0648\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u062c\u0627 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0622\u0646\u0627\u0644\u06cc\u0632 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0648\u0646-\u0646\u06cc\u0648\u0645\u0646<\/em><\/strong> \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0628\u0633\u0637 \u0633\u0631\u06cc \u062a\u06cc\u0644\u0648\u0631<\/em><\/strong> ui<\/sub>n<\/sup><\/em><\/strong> \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (4) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f:<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (4)\u00a0 G<\/em><\/strong> \u0636\u0631\u06cc\u0628 \u0631\u0634\u062f \u06cc\u0627 \u0647\u0645\u0627\u0646 \u0628\u0632\u0631\u06af\u06cc \u062f\u0627\u0645\u0646\u0647 \u0648 p<\/em><\/strong> \u0639\u062f\u062f \u0645\u0648\u062c \u062f\u0631 \u062c\u0647\u062a x<\/em><\/strong> \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0627\u0628\u0637\u0647 \u0641\u0648\u0642\u060c \u0645\u0639\u0627\u062f\u0644\u0647 (3) \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631 \u0642\u0627\u0644\u0628 \u0628\u0633\u0637 \u0633\u0631\u06cc \u0641\u0648\u0631\u06cc\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (5) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u0628\u0627 \u0641\u0627\u06a9\u062a\u0648\u0631 \u06af\u06cc\u0631\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0631\u0627\u0628\u0637\u0647 (6) \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0634\u0631\u0637 \u0644\u0627\u0632\u0645 \u0648 \u06a9\u0627\u0641\u06cc \u0628\u0631\u0627\u06cc \u0635\u0627\u062f\u0642 \u0628\u0648\u062f\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (6)\u060c \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0631\u0627\u0628\u0637\u0647 (7) \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f. \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u062f\u0627\u0645\u0646\u0647 p<\/em><\/strong> \u0628\u06cc\u0646 \u0645\u062b\u0628\u062a \u0648 \u0645\u0646\u0641\u06cc \u0628\u06cc\u200c\u0646\u0647\u0627\u06cc\u062a \u0627\u0633\u062a \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u2013p\u0394x=\u03b8<\/em><\/strong> \u0648 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0648\u0627\u0628\u0637 \u062c\u0628\u0631 \u0645\u062e\u062a\u0644\u0637 \u0645\u0639\u0627\u062f\u0644\u0647 (8) \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f.<\/span><\/p>\n

\"\u067e\u0627\u06cc\u062f\u0627\u0631\u06cc<\/p>\n

\u062f\u0631 \u0646\u062a\u06cc\u062c\u0647\u060c \u0628\u0647 \u0627\u0632\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 C\u22641<\/em><\/strong>\u060c \u0627\u06cc\u0646 \u0631\u0648\u0634 \u06cc\u06a9 \u0631\u0648\u0634 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a. \u0645\u062d\u062f\u0648\u062f\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc C<\/em><\/strong> \u062f\u0631 \u0634\u06a9\u0644 (1) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u0627\u0646\u062f\u0627\u0632\u0647 \u0634\u0639\u0627\u0639 \u062f\u0627\u06cc\u0631\u0647 \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631\u060c G<\/em>\u060c\u00a0 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0648\u0627\u062d\u062f \u0628\u0627\u0634\u062f\u060c \u0631\u0648\u0634 \u0635\u0631\u06cc\u062d \u062a\u0641\u0627\u0636\u0644 FTBS \u067e\u0627\u06cc\u062f\u0627\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u067e\u0627\u0631\u0627\u0645\u062a\u0631 C<\/em><\/strong> \u0631\u0627 \u0627\u0635\u0637\u0644\u0627\u062d\u0627\u064b \u0639\u062f\u062f \u06a9\u0648\u0631\u0627\u0646\u062a(Courant Number) \u06cc\u0627 \u0639\u062f\u062f CFL<\/strong>: Courant-Fredrich-Levy \u0646\u06cc\u0632 \u0645\u06cc\u200c\u0646\u0627\u0645\u0646\u062f.<\/span><\/p>\n

\"\u0645\u062d\u062f\u0648\u062f\u0647<\/p>\n

\u0634\u06a9\u0644-1: \u0645\u062d\u062f\u0648\u062f\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u062f\u0631 \u0641\u0636\u0627\u06cc \u0645\u062e\u062a\u0644\u0637.<\/strong><\/span><\/h6>\n

\u0645\u062b\u0627\u0644-1 \u06a9\u0647 \u062f\u0631 \u0642\u0633\u0645\u062a \u0642\u0628\u0644 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647\u060c \u062f\u0631 \u0627\u06cc\u0646 \u0642\u0633\u0645\u062a \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 FTBS \u0635\u0631\u06cc\u062d \u0628\u0635\u0648\u0631\u062a \u0639\u062f\u062f\u06cc \u062d\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0634\u06a9\u0644\u0647\u0627\u06cc (2) \u0648 (3) \u0628\u06cc\u0627\u0646\u06af\u0631 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062f\u0631 \u0634\u06a9\u0644 (2) \u0686\u06af\u0648\u0646\u06af\u06cc \u062d\u0631\u06a9\u062a \u0645\u0648\u062c \u062f\u0631 \u0635\u0641\u062d\u0647 (x,t)<\/em><\/strong> \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0634\u06a9\u0644 (2-\u0627\u0644\u0641) \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0632\u0645\u0627\u0646 \u0637\u0648\u0644 \u0645\u0648\u062c (\u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u0648\u062c \u062f\u0631 \u062c\u0647\u062a x<\/em><\/strong>) \u0627\u0641\u0632\u0627\u06cc\u0634 \u0648 \u062f\u0627\u0645\u0646\u0647 \u0622\u0646 (\u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u0648\u062c \u062f\u0631 \u062c\u0647\u062a z<\/em><\/strong>) \u06a9\u0627\u0647\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. \u062f\u0631 \u062d\u0627\u0644\u06cc\u06a9\u0647 \u062f\u0631 \u0634\u06a9\u0644 (2-\u0628) \u0647\u0645 \u0637\u0648\u0644 \u0645\u0648\u062c \u0648 \u0647\u0645 \u062f\u0627\u0645\u0646\u0647 \u0622\u0646 \u062b\u0627\u0628\u062a \u0628\u0627\u0642\u06cc \u0645\u06cc\u200c\u0645\u0627\u0646\u062f. \u0639\u0644\u062a \u0627\u06cc\u0646 \u0627\u0645\u0631\u060c \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0642\u062f\u0627\u0631 C \u0627\u0633\u062a. \u0647\u0631\u0686\u0647 \u0645\u0642\u062f\u0627\u0631 C \u0628\u0647 \u0645\u0642\u062f\u0627\u0631 \u06cc\u06a9 \u0646\u0632\u062f\u06cc\u06a9\u062a\u0631 \u0628\u0627\u0634\u062f\u060c \u062d\u0644 \u0639\u062f\u062f\u06cc \u062d\u0627\u0635\u0644 \u0627\u0632 \u0631\u0648\u0634 \u0635\u0631\u06cc\u062d FTBS \u062f\u0642\u06cc\u0642\u062a\u0631 \u0628\u0648\u062f\u0647 \u0648 \u0628\u0647 \u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0646\u0632\u062f\u06cc\u06a9\u062a\u0631 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-2: \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u06cc\u06a9 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 FTBS \u0635\u0631\u06cc\u062d. \u0627\u0644\u0641: C=0.45\u060c \u0628: C=0.9996.<\/strong><\/span><\/h6>\n

\u062f\u0631 \u0634\u06a9\u0644 (3) \u0645\u0648\u0642\u0639\u06cc\u062a \u0648 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u0648\u062c \u062f\u0631 \u0632\u0645\u0627\u0646 45\/0 \u062b\u0627\u0646\u06cc\u0647 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0646\u06cc\u0632 \u0645\u0634\u062e\u0635 \u0627\u0633\u062a\u060c \u062f\u0631 \u0632\u0645\u0627\u0646 0.45 \u062b\u0627\u0646\u06cc\u0647 \u062d\u0644 \u062d\u0627\u0635\u0644 \u0627\u0632 C=0.45<\/em><\/strong> \u062f\u0627\u0631\u0627\u06cc \u0637\u0648\u0644 \u0645\u0648\u062c \u0628\u0632\u0631\u06af\u062a\u0631 \u0648 \u062f\u0627\u0645\u0646\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0646\u0633\u0628\u062a \u0628\u0647 \u062d\u0644 \u062d\u0627\u0635\u0644 \u0627\u0632 C=0.9996<\/em><\/strong> \u0648 \u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0631\u0627\u0633\u0627\u0633 C=0.9996<\/em><\/strong> \u0646\u06cc\u0632 \u062f\u0631 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0627\u0631\u0627\u0626\u0647 \u0634\u062f\u0647 \u0648 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u0642\u062f\u0627\u0631 C<\/em><\/strong> \u062a\u0627 \u06cc\u06a9\u060c \u062c\u0648\u0627\u0628\u0647\u0627 \u062f\u0642\u06cc\u0642\u062a\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

\"\u0645\u0642\u0627\u06cc\u0633\u0647<\/p>\n

\u0634\u06a9\u0644-3: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 FTBS \u0635\u0631\u06cc\u062d \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0.45 S.<\/strong><\/span><\/h6>\n

\u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0631\u0648\u0634 FTBS \u0635\u0631\u06cc\u062d \u06cc\u06a9 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0627\u0633\u062a \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062e\u0637\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u0627\u0632 \u0646\u0648\u0639 \u062e\u0637\u0627\u06cc \u0627\u0636\u0645\u062d\u0644\u0627\u0644\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0644\u0630\u0627 \u0627\u0646\u062a\u0638\u0627\u0631 \u0628\u0631 \u0627\u06cc\u0646\u0633\u062a \u06a9\u0647 \u062e\u0637\u0627\u06cc \u062d\u0627\u0635\u0644 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0635\u0648\u0631\u062a \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0631 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0627\u0645\u0646\u0647 \u0638\u0627\u0647\u0631 \u0634\u0648\u062f. \u0627\u06cc\u0646 \u067e\u062f\u06cc\u062f\u0647 \u0631\u0627 \u0628\u0648\u0636\u0648\u062d \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631 \u0634\u06a9\u0644\u0647\u0627\u06cc (2) \u0648 (3) \u0645\u0634\u0627\u0647\u062f\u0647 \u0646\u0645\u0648\u062f.<\/span><\/p>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634 \u0635\u0631\u06cc\u062d \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0645\u06a9\u0627\u0646 (FTFS: Forward in Time and Forward in Space )<\/strong><\/span><\/span><\/h4>\n

\u0631\u0648\u0634 FTFS \u0635\u0631\u06cc\u062d \u0627\u0648\u06cc\u0644\u0631 \u0628\u0631\u0627\u0633\u0627\u0633 \u062a\u0642\u0631\u06cc\u0628 \u062a\u0641\u0627\u0636\u0644 \u067e\u06cc\u0634\u0631\u0648 \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062f\u0648 \u062a\u0631\u0645 \u0632\u0645\u0627\u0646\u06cc \u0648 \u0645\u06a9\u0627\u0646\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u06a9\u0644\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u062d\u0627\u06a9\u0645 \u062f\u0631 \u0645\u062b\u0627\u0644 (1) \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (9) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0641\u0648\u0642\u060c \u062a\u0631\u0645 \u0627\u0648\u0644 \u0633\u0645\u062a \u0686\u067e \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0634\u06a9\u0644\u06cc \u0646\u062f\u0627\u0631\u062f\u060c \u0686\u0631\u0627\u06a9\u0647 \u0627\u0632 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc \u0642\u0628\u0644\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u0645\u0627 \u062a\u0631\u0645 \u062f\u0648\u0645 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0645\u0634\u06a9\u0644 \u0633\u0627\u0632 \u0628\u0627\u0634\u062f. \u0639\u0644\u062a \u0627\u06cc\u0646 \u0627\u0645\u0631 \u0627\u06cc\u0646\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0628\u0631\u0627\u0633\u0627\u0633 \u0645\u06a9\u0627\u0646\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f (un<\/sup>i+1<\/sub><\/em><\/strong>) \u06a9\u0647 \u0634\u0646\u0627\u062e\u062a \u062f\u0642\u06cc\u0642\u06cc \u0627\u0632 \u0622\u0646 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f (\u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0648\u062f\u0646). \u0628\u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u0644\u0627\u0632\u0645\u0633\u062a \u06a9\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0622\u0646 \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u06cc\u0631\u062f. \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0628\u0633\u0637 \u0633\u0631\u06cc \u0641\u0648\u0631\u06cc\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (9) \u0631\u0627 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (10) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647\u060c \u0628\u0631\u0627\u06cc \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 (11) \u062d\u0627\u06a9\u0645 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u062a\u062d\u0644\u06cc\u0644 \u0627\u0648\u0644 \u0648\u0646-\u0646\u06cc\u0648\u0645\u0646 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u06cc \u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0645\u06a9\u0627\u0646\u200c\u067e\u0630\u06cc\u0631 \u0646\u06cc\u0633\u062a. \u0627\u0644\u0628\u062a\u0647\u060c \u0648\u0642\u062a\u06cc \u0635\u062d\u0628\u062a \u0627\u0632 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0628\u0647 \u0645\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0622\u06cc\u062f\u060c \u0645\u0646\u0638\u0648\u0631 \u0627\u06cc\u0646\u0633\u062a \u06a9\u0647 \u0633\u0631\u06cc \u0641\u0648\u0631\u06cc\u0647 \u062d\u0627\u0635\u0644\u0647 \u06cc\u06a9 \u0633\u0631\u06cc \u0648\u0627\u06af\u0631\u0627 \u0628\u0648\u062f\u0647 \u0648 \u0645\u0642\u062f\u0627\u0631 \u067e\u0627\u0633\u062e\u0647\u0627 \u062f\u0631 \u0647\u0631 \u06af\u0627\u0645 \u0632\u0645\u0627\u0646\u06cc \u0628\u0634\u062f\u062a \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0628\u0647\u062a\u0631\u060c \u062d\u0644 \u0639\u062f\u062f\u06cc \u0627\u0646\u062c\u0627\u0645 \u0634\u062f\u0647 \u0628\u0631 \u0631\u0648\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062a\u0646\u0647\u0627 \u0628\u0631\u0627\u06cc \u0632\u0645\u0627\u0646 \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0648\u0686\u06a9 (\u06a9\u0645\u062a\u0631 \u0627\u0632 0.5 \u062b\u0627\u0646\u06cc\u0647) \u062f\u0631 \u0634\u06a9\u0644 (4) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0646\u0648\u0633\u0627\u0646\u0627\u062a \u0628\u0633\u06cc\u0627\u0631 \u0634\u062f\u06cc\u062f \u062f\u0631 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0627\u0645\u0646\u0647 \u0628\u06cc\u0627\u0646\u06af\u0631 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0631\u0648\u0634 \u062d\u0644 \u0648 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-4: \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0627\u0641-\u062a\u06cc-\u0627\u0641-\u0627\u0633 \u06a9\u0647 \u0646\u0634\u0627\u0646\u06af\u0631 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631 \u0628\u0648\u062f\u0646 \u0622\u0646 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/strong><\/span><\/h6>\n

\u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646\u06a9\u0647 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634 \u0635\u0631\u06cc\u062d \u0627\u0648\u06cc\u0644\u0631 \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646 (Forward in Time and Centered in Space (FTCS) )<\/strong><\/span><\/span><\/h4>\n

\u0631\u0648\u0634 FTCS \u0635\u0631\u06cc\u062d \u0627\u0648\u06cc\u0644\u0631 \u0627\u0632 \u06cc\u06a9 \u062a\u0641\u0627\u0636\u0644 \u067e\u06cc\u0634\u0631\u0648 \u0628\u0631\u0627\u06cc \u0632\u0645\u0627\u0646 \u0648 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u0628\u0631\u0627\u06cc \u0645\u06a9\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u06af\u0633\u0633\u062a\u0647 \u0633\u0627\u0632\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u062b\u0627\u0644 (1) \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (12) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0646\u06cc\u0632 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u062f\u0627\u0631\u062f. \u0644\u0627\u0632\u0645 \u0628\u0647 \u062a\u0648\u0636\u06cc\u062d \u0627\u0633\u062a \u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc \u0631\u0648\u0634 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f\u06cc \u0628\u0627\u06cc\u062f \u0627\u0632 \u0641\u06cc\u0632\u06cc\u06a9 \u0645\u0633\u0626\u0644\u0647 \u067e\u06cc\u0631\u0648\u06cc \u06a9\u0631\u062f\u0647 \u0648 \u0628\u0627 \u0622\u0646 \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f. \u0627\u06af\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u062f\u0631 \u0647\u0631 \u0645\u0633\u0626\u0644\u0647\u200c\u0627\u06cc \u0635\u0627\u062f\u0642 \u0646\u0628\u0627\u0634\u062f\u060c \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0622\u0646 \u0631\u0648\u0634 \u0645\u0633\u0626\u0644\u0647 \u0633\u0627\u0632 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0628\u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0646\u06cc\u0632 \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a. \u0628\u0633\u0637 \u0633\u0631\u06cc \u0641\u0648\u0631\u06cc\u0647 \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0627 \u0645\u0639\u0627\u062f\u0644\u0647 (12) \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (13) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0627\u0644\u0628\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (13) \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (14) \u0646\u06cc\u0632 \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (14)\u060c G<\/em><\/strong> \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0647 (15) \u0642\u0627\u0628\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u0631\u0627\u0628\u0637\u0647 \u0641\u0648\u0642 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 G<\/em><\/strong> \u0647\u0645\u0648\u0627\u0631\u0647 \u0628\u0632\u0631\u06af\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u0635\u0641\u0631 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644\u060c \u0631\u0648\u0634 \u06cc\u0627\u062f \u0634\u062f\u0647 \u06cc\u06a9 \u0631\u0648\u0634 \u0628\u06cc \u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631 \u0648 \u063a\u06cc\u0631 \u0642\u0627\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

<\/a>\u0631\u0648\u0634 \u0644\u0627\u06a9\u0633 (Lax Scheme)<\/strong><\/span><\/span><\/h4>\n

\u062f\u0631 \u0635\u0648\u0631\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 FTCS \u0635\u0631\u06cc\u062d \u0627\u0648\u06cc\u0644\u0631 \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644\u060c \u0627\u06af\u0631 \u0627\u0632 \u0645\u0642\u062f\u0627\u0631 \u0645\u062a\u0648\u0633\u0637 \u00a0\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f\u060c \u0645\u0639\u0627\u062f\u0644\u0647 (12) \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (16) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0628\u0633\u0637 \u0633\u0631\u06cc \u062a\u06cc\u0644\u0648\u0631 \u0648 \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0622\u0646\u0627\u0644\u06cc\u0632 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0631\u0627\u0628\u0637\u0647 (17) \u0645\u062f \u0646\u0638\u0631 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (17)\u060c \u0628\u0631\u0627\u06cc \u0628\u0631\u0642\u0631\u0627\u0631\u06cc \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0644\u0627\u0632\u0645\u0633\u062a \u0627\u0646\u062f\u0627\u0632\u0647 G \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (18) \u06a9\u0648\u0686\u06a9\u062a\u0631 \u06cc\u0627 \u0645\u0633\u0627\u0648\u06cc \u06cc\u06a9 \u0628\u0627\u0634\u062f (\u0631\u0627\u0628\u0637\u0647 19). \u0628\u0627 \u0646\u06af\u0627\u0647\u06cc \u062f\u0642\u06cc\u0642\u200c\u062a\u0631 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (16) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0634\u0627\u0647\u062f\u0647 \u0646\u0645\u0648\u062f \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062a\u0631\u0645 \u0627\u0648\u0644 \u0633\u0645\u062a \u0686\u067e \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0631\u0627\u0628\u0637\u0647 (20) \u0628\u0631\u0642\u0631\u0627\u0631 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0648\u0627\u0628\u0637 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0647 \u062a\u0631\u0645 \u0644\u0632\u062c\u062a \u0645\u0635\u0646\u0648\u0639\u06cc \u062f\u0631 \u062c\u0648\u0647\u0631\u0647 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f. \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0648\u06cc\u0698\u06af\u06cc \u0627\u06cc\u0646 \u062a\u0631\u0645 \u0627\u06cc\u0646\u0633\u062a \u06a9\u0647 \u0628\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u06a9\u0645\u06a9 \u06a9\u0631\u062f\u0647 \u0648 \u062e\u0637\u0627\u0647\u0627 \u0631\u0627 \u0628\u0637\u0648\u0631 \u0686\u0634\u0645\u06af\u06cc\u0631\u06cc \u06a9\u0627\u0647\u0634 \u062f\u0627\u062f\u0647 \u0648 \u0627\u0632 \u0628\u06cc\u0646 \u0645\u06cc\u200c\u0628\u0631\u062f (\u0686\u0631\u0627\u06a9\u0647 \u0644\u0632\u062c\u062a \u0627\u062b\u0631 \u0635\u0627\u0641 \u06a9\u0631\u062f\u0646 \u067e\u06cc\u06a9\u200c\u0647\u0627 \u06cc\u0627 \u0647\u0645\u0627\u0646 \u062a\u06cc\u0632\u06cc\u200c\u0647\u0627 \u0631\u0627 \u062f\u0631 \u062d\u0644 \u062f\u0627\u0631\u062f). \u0627\u0645\u0627 \u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u0622\u0646 \u0646\u0628\u0627\u06cc\u062f \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647\u200c\u0627\u06cc \u0628\u0632\u0631\u06af \u0628\u0627\u0634\u062f \u06a9\u0647 \u0645\u0627\u0647\u06cc\u062a \u062c\u0631\u06cc\u0627\u0646 \u0631\u0627\u00a0 \u0639\u0648\u0636 \u06a9\u0646\u062f. \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u062b\u0627\u0644-1 \u062f\u0631 \u0634\u06a9\u0644\u0647\u0627\u06cc (5) \u0648 (6) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\u062f\u0631\u0634\u06a9\u0644 (5) \u0686\u06af\u0648\u0646\u06af\u06cc \u062d\u0631\u06a9\u062a \u0645\u0648\u062c \u062f\u0631 \u0635\u0641\u062d\u0647 (x,t<\/em><\/strong>) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0645\u0634\u062e\u0635 \u0627\u0633\u062a\u060c \u0628\u0647 \u0627\u0632\u0627\u06cc \u0645\u0642\u062f\u0627\u0631 C=0.9996 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0628\u0627 \u062c\u0648\u0627\u0628 \u062f\u0642\u06cc\u0642 \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0634\u062a\u0647 \u0648 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0628\u0627 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a. \u0627\u0645\u0627 \u0628\u0631\u0627\u06cc C=0.45 \u0628\u0627 \u06af\u0630\u0634\u062a \u0632\u0645\u0627\u0646 \u0627\u0632 \u062f\u0642\u062a \u062c\u0648\u0627\u0628\u0647\u0627 \u06a9\u0627\u0633\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u06af\u0633\u0633\u062a\u0647 \u0633\u0627\u0632\u06cc \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0627\u0632 \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u062e\u0637\u0627\u0647\u0627 \u062f\u0631 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0627\u0645\u0646\u0647 \u062c\u0648\u0627\u0628 \u0638\u0627\u0647\u0631 \u0634\u062f\u0647 \u0627\u0633\u062a (\u0634\u06a9\u0644\u0647\u0627\u06cc 5-\u0627\u0644\u0641 \u0648 6). \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0639\u0644\u062a \u06a9\u0627\u0647\u0634 \u0628\u06cc\u0634 \u0627\u0632 \u062d\u062f \u062f\u0627\u0645\u0646\u0647 \u0645\u0648\u062c \u0648 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0637\u0648\u0644 \u0645\u0648\u062c \u0622\u0646 \u062f\u0631 \u0634\u06a9\u0644 (5-\u0627\u0644\u0641) \u0646\u0633\u0628\u062a \u0628\u0647 \u0631\u0648\u0634 FTBS \u0635\u0631\u06cc\u062d\u060c (\u0634\u06a9\u0644 3) \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0646\u0627\u0634\u06cc \u0627\u0632 \u0648\u062c\u0648\u062f \u062a\u0631\u0645 \u0644\u0632\u062c\u062a \u0645\u0635\u0646\u0648\u0639\u06cc \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0627\u0636\u0645\u062d\u0644\u0627\u0644 \u062c\u0648\u0627\u0628\u0647\u0627 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u0627\u0634\u06cc \u0627\u0632\u00a0 \u062a\u0641\u0627\u0648\u062a \u062a\u0639\u0631\u06cc\u0641 \u0639\u062f\u062f \u06a9\u0648\u0631\u0627\u0646\u062a\u060c C\u060c (\u0627\u0644\u0628\u062a\u0647 \u0628\u0627 \u062a\u0623\u062b\u06cc\u0631 \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0646\u0633\u0628\u062a \u0628\u0647 \u062a\u0631\u0645 \u0644\u0632\u062c\u062a \u0645\u0635\u0646\u0648\u0639\u06cc) \u062f\u0627\u0646\u0633\u062a. \u0627\u06cc\u0646 \u0627\u062e\u062a\u0644\u0627\u0641 \u062f\u0631 \u0634\u06a9\u0644 (7) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-5: \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0644\u0627\u06a9\u0633. \u0627\u0644\u0641: C=0.45\u060c \u0628: C=0.9996.<\/span><\/strong><\/h6>\n

\"\u0645\u0642\u0627\u06cc\u0633\u0647<\/p>\n

\u0634\u06a9\u0644-6: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0644\u0627\u06a9\u0633 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u0639\u062f\u0627\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0.45 S.<\/span><\/strong><\/h6>\n

\"\u0645\u0642\u0627\u06cc\u0633\u0647<\/p>\n

\u0634\u06a9\u0644-7: \u0627\u062e\u062a\u0644\u0627\u0641 \u0628\u06cc\u0646 \u0631\u0648\u0634\u0647\u0627\u06cc FTBS \u0648 \u0644\u0627\u06a9\u0633 \u0628\u0627 \u0639\u062f\u062f \u06a9\u0648\u0631\u0627\u0646\u062a C=0.45 \u062f\u0631 \u0632\u0645\u0627\u0646 \u00a0t=0.45 S.<\/span><\/strong><\/h6>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634 \u0644\u0627\u06a9\u0633-\u0648\u0646\u062f\u0631\u0648\u0641 (Lax-Wendroff Scheme)<\/strong><\/span><\/span><\/h4>\n

\u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0644\u0627\u06a9\u0633-\u0648\u0646\u062f\u0631\u0648\u0641 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0628\u0633\u0637 \u0633\u0631\u06cc \u062a\u06cc\u0644\u0648\u0631 \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a (21 \u06cc\u0627 22) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0648 \u0631\u0648\u0627\u0628\u0637 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (23)\u060c \u0645\u0639\u0627\u062f\u0644\u0647 (22) \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0635\u0648\u0631\u062a \u0631\u0627\u0628\u0637\u0647 (24) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u062f\u0631 \u062d\u0642\u06cc\u0642\u062a \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0648\u0627\u0628\u0637 22 \u0648 23\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u06cc\u0627 \u0647\u0645\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0628\u0627 \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0647 \u0631\u0627\u0628\u0637\u0647 (24) \u0645\u06cc\u200c\u0631\u0633\u06cc\u0645 \u06a9\u0647 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (25) \u0647\u0645 \u0646\u0648\u0634\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u0631\u0648\u0634 \u0645\u0630\u06a9\u0648\u0631 \u0627\u0632 \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u0632\u0645\u0627\u0646\u06cc \u0648 \u0645\u06a9\u0627\u0646\u06cc<\/strong><\/span> \u0628\u0647\u0631\u0647 \u0645\u06cc\u200c\u0628\u0631\u062f \u06a9\u0647 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062f\u0642\u062a \u0645\u0646\u0627\u0633\u0628\u06cc \u062f\u0627\u0631\u062f. \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u062b\u0627\u0644-1 \u062f\u0631 \u0634\u06a9\u0644\u0647\u0627\u06cc (8) \u0648 (9) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-8: \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0644\u0627\u06a9\u0633-\u0648\u0646\u062f\u0631\u0648\u0641. \u0627\u0644\u0641: C=0.45\u060c \u0628: C=0.9996.<\/strong><\/span><\/h6>\n

\"\u0628\u0631\u0631\u0633\u06cc<\/p>\n

\u0634\u06a9\u0644-9: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0644\u0627\u06a9\u0633-\u0648\u0646\u062f\u0631\u0648\u0641 \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0.45 S.<\/strong><\/span><\/h6>\n

\u062f\u0631 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (8) \u0648 (9) \u0628\u0648\u0636\u0648\u062d \u0645\u0634\u062e\u0635 \u0627\u0633\u062a \u06a9\u0647 \u0686\u0648\u0646 \u0627\u0632 \u062c\u0645\u0644\u0647 \u0641\u0631\u062f (\u062c\u0645\u0644\u0647 \u0633\u0648\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (22) \u06cc\u0627 \u0647\u0645\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (24)) \u062f\u0631 \u0628\u0633\u0637 \u0633\u0631\u06cc \u062a\u06cc\u0644\u0648\u0631 \u0642\u0637\u0639 \u0634\u062f\u0647\u060c \u062e\u0637\u0627\u06cc \u067e\u062f\u06cc\u062f \u0622\u0645\u062f\u0647 \u06cc\u06a9 \u062e\u0637\u0627\u06cc \u0646\u0648\u0633\u0627\u0646\u06cc \u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc \u0645\u0630\u06a9\u0648\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0647 \u062e\u0637\u0627\u0647\u0627\u06cc \u0646\u0648\u0633\u0627\u0646\u06cc \u0631\u0648\u06cc \u062f\u0627\u0645\u0646\u0647 \u062d\u0644 \u062a\u0623\u062b\u06cc\u0631 \u0686\u0646\u062f\u0627\u0646\u06cc \u0646\u062f\u0627\u0631\u062f \u0648 \u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u062e\u0637\u0627\u06cc \u062f\u0627\u0645\u0646\u0647 \u0628\u0647 \u062c\u0648\u0627\u0628 \u062f\u0642\u06cc\u0642 \u0646\u0632\u062f\u06cc\u06a9\u062a\u0631 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634 \u0645\u06a9\u200c\u06a9\u0648\u0631\u0645\u06a9(MacCormack Scheme)<\/span><\/span><\/strong><\/h4>\n

\u0631\u0648\u0634 \u0645\u06a9\u200c\u06a9\u0648\u0631\u0645\u06a9 \u0631\u0648\u0634\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0637\u0648\u0631 \u06af\u0633\u062a\u0631\u062f\u0647 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062c\u0631\u06cc\u0627\u0646 \u0633\u06cc\u0627\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062f\u0631 \u0645\u0633\u0627\u0626\u0644 \u062e\u0637\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634 \u0644\u0627\u06a9\u0633-\u0648\u0646\u062f\u0631\u0648\u0641 \u0628\u0648\u062f\u0647 \u0648 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0648 \u0631\u0648\u0634 \u0645\u062b\u0644 \u0647\u0645 \u0627\u0633\u062a. \u0627\u0645\u0627\u060c \u062f\u0631 \u0645\u0633\u0627\u0626\u0644 \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0631\u0648\u0634 \u0645\u06a9\u200c\u06a9\u0648\u0631\u0645\u06a9 \u0628\u0647 \u0645\u0631\u0627\u062a\u0628 \u0627\u0632 \u062f\u0642\u062a \u0628\u06cc\u0634\u062a\u0631\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

\u0631\u0648\u0634 \u0645\u06a9\u200c\u06a9\u0648\u0631\u0645\u06a9 \u062f\u0627\u0631\u0627\u06cc \u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0647\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u06cc\u06a9 \u0645\u0631\u062d\u0644\u0647 \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0634\u0627\u0645\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u067e\u06cc\u0634\u06af\u0648(Predictor) (\u0631\u0627\u0628\u0637\u0647 26) \u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u062a\u0635\u062d\u06cc\u062d \u06a9\u0646\u0646\u062f\u0647(Corrector) \u00a0(\u0631\u0627\u0628\u0637\u0647 27) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0639\u0644\u0627\u0645\u062a (\u00af) \u0628\u06cc\u0627\u0646\u06af\u0631 \u0645\u0642\u062f\u0627\u0631 \u0645\u0648\u0642\u062a\u06cc \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a. \u0627\u0645\u0627 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0648\u0645 \u06cc\u0627 \u0647\u0645\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u062a\u0635\u062d\u06cc\u062d \u06a9\u0646\u0646\u062f\u0647 \u0627\u0632 \u062a\u0641\u0627\u0636\u0644 \u067e\u06cc\u0634\u0631\u0648 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647\u060c \u0641\u0631\u0645 \u0646\u0647\u0627\u06cc\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u062a\u0635\u062d\u06cc\u062d \u06a9\u0646\u0646\u062f\u0647 \u0628\u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0631\u0627\u0628\u0637\u0647 (28) \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u00a0\u0627\u06af\u0631\u0686\u0647 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0631\u0648\u0634 \u0645\u06a9\u200c\u06a9\u0648\u0631\u0645\u06a9 \u06a9\u0645\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u0647\u0645 \u0627\u0632 \u0646\u0638\u0631 \u0645\u06a9\u0627\u0646\u06cc \u0648 \u0647\u0645 \u0627\u0632 \u0646\u0638\u0631 \u0632\u0645\u0627\u0646\u06cc \u0627\u0632 \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (26) \u0648 (28) \u0645\u0634\u062e\u0635 \u0627\u0633\u062a\u060c \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u067e\u06cc\u0634\u06af\u0648\u06cc\u06cc \u0627\u0632 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u067e\u0633\u0631\u0648 \u0628\u0631\u0627\u06cc u\/\u2202x\u2202<\/em><\/strong> \u0648 \u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u062a\u0635\u062d\u06cc\u062d \u0627\u0632 \u062a\u0641\u0627\u0636\u0644 \u067e\u06cc\u0634\u0631\u0648 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u062a\u0641\u0627\u0636\u0644\u200c\u0647\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0639\u06a9\u0633 \u0646\u06cc\u0632 \u0628\u06a9\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u0648\u062f \u06a9\u0647 \u062f\u0631 \u0628\u0631\u062e\u06cc \u0645\u0633\u0627\u0626\u0644 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u062a\u0648\u0635\u06cc\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644-1 \u062f\u0631 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (10) \u0648 (11) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0627 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (10 \u0648 11) \u0628\u0627 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (8 \u0648 9) \u0645\u0634\u0627\u0647\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0631\u0648\u0634 \u0645\u06a9 \u06a9\u0648\u0631\u0645\u06a9 \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0647\u0645\u0627\u0646\u0646\u062f \u0631\u0648\u0634 \u0644\u0627\u06a9\u0633-\u0648\u0646\u062f\u0631\u0648\u0641 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-10: \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0645\u06a9 \u06a9\u0648\u0631\u0645\u06a9. \u0627\u0644\u0641: C=0.45\u060c \u0628: C=0.9996.<\/span><\/strong><\/h6>\n

\"\u0628\u0631\u0631\u0633\u06cc<\/p>\n

\u0634\u06a9\u0644-11: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0645\u06a9\u200c\u06a9\u0648\u0631\u0645\u06a9 \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0.45 S.<\/span><\/strong><\/h6>\n

<\/a>\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c<\/strong><\/span><\/span><\/h3>\n

\u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u062e\u0637\u06cc \u0627\u0633\u062a\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0646\u062a\u0638\u0627\u0631 \u062f\u0627\u0634\u062a \u06a9\u0647 \u062f\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0628\u06cc\u200c\u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0628\u0627\u0634\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062f\u0631 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0645\u0633\u0627\u0626\u0644 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u062e\u0627\u0635\u06cc \u062f\u0631 \u0627\u0646\u062a\u062e\u0627\u0628 \u0394t<\/em><\/strong> \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f. \u0627\u0644\u0628\u062a\u0647 \u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u060c \u0628\u0627 \u0627\u06cc\u0646\u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0642\u062f\u0627\u0631 \u0394t<\/em><\/strong> \u0631\u0627 \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u062f\u0644\u062e\u0648\u0627\u0647 \u0628\u0632\u0631\u06af \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u060c \u0627\u0645\u0627 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc\u06a9\u0647 \u0645\u0634\u0627\u0647\u062f\u0647 \u062c\u0632\u0626\u06cc\u0627\u062a \u0646\u0633\u0628\u062a \u0628\u0647 \u06af\u0630\u0634\u062a \u0632\u0645\u0627\u0646 \u0645\u0637\u0644\u0648\u0628 \u0628\u0627\u0634\u062f\u060c \u0644\u0627\u0632\u0645\u0633\u062a \u0394t<\/em><\/strong> \u0631\u0627 \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u0644\u0627\u0632\u0645 \u06a9\u0648\u0686\u06a9 \u0627\u0646\u062a\u062e\u0627\u0628 \u0646\u0645\u0648\u062f. \u062f\u0631 \u0628\u062d\u062b \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0631\u0648\u0634\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc\u060c \u0647\u0631\u0642\u062f\u0631 \u0628\u062a\u0648\u0627\u0646 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0628\u06cc\u0634\u062a\u0631\u06cc \u0631\u0627 \u0647\u0645\u0632\u0645\u0627\u0646 \u062f\u0631\u06af\u06cc\u0631 \u0646\u0645\u0648\u062f\u060c \u0622\u0646\u06af\u0627\u0647 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u062d\u0644 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u067e\u0633\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646 (BTCS) \u0627\u0648\u06cc\u0644\u0631<\/strong><\/span> \u0648 \u06a9\u0631\u0627\u0646\u06a9 \u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 (Cranck-Nicolson) <\/strong><\/span>\u0627\u0632 \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0628\u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f \u06a9\u0647 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0628\u0647 \u0622\u0646\u0647\u0627 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634 BTCS \u0627\u0648\u06cc\u0644\u0631<\/strong><\/span><\/span><\/h4>\n

\u0631\u0648\u0634 BTCS \u06cc\u06a9 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u067e\u0633\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0686\u06af\u0648\u0646\u06af\u06cc \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (29) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.\u0627\u06af\u0631 \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0647 \u0641\u0648\u0642 \u062f\u0631 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u0634\u0628\u06a9\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f\u060c \u06cc\u06a9 \u062f\u0633\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u062c\u0628\u0631\u06cc \u062e\u0637\u06cc \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0622\u0646\u0631\u0627 \u0628\u0634\u06a9\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0646\u06cc\u0632 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f \u06a9\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0636\u0631\u0627\u0626\u0628 \u0622\u0646 \u0633\u0647 \u0642\u0637\u0631\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0631\u0627\u06cc \u0622\u0646\u0627\u0644\u06cc\u0632 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0647\u0645\u0627\u0646 \u0631\u0648\u0634 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0628\u062e\u0634 \u0642\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (29) \u0631\u0627 \u0628\u0635\u0648\u0631\u062a \u0631\u0627\u0628\u0637\u0647 (30) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f.\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (30)\u060c \u0631\u0627\u0628\u0637\u0647 (31) \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0628\u0632\u0631\u06af\u06cc G \u0628\u0631\u0627\u0628\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (32) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u0628\u062f\u06cc\u0647\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (32) \u0647\u0645\u0648\u0627\u0631\u0647 \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0627\u0632 \u06cc\u06a9 \u0628\u0648\u062f\u0647 \u0648 \u0644\u0630\u0627 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u06cc\u200c\u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a. \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u062d\u0644 \u0645\u062b\u0627\u0644-1 \u062f\u0631 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (12 \u0648 13) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644\u200c\u0647\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0647 \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u0642\u062f\u0627\u0631 \u0639\u062f\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641\u060c \u0628\u0627 \u06af\u0630\u0634\u062a \u0632\u0645\u0627\u0646 \u0645\u0642\u062f\u0627\u0631 \u062e\u0637\u0627\u06cc \u0639\u062f\u062f\u06cc \u0646\u06cc\u0632 \u0628\u06cc\u0634\u062a\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-12: \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u0628\u06cc-\u062a\u06cc-\u0633\u06cc-\u0627\u0633. \u0627\u0644\u0641: C=0.45\u060c \u0628: C=0.9996.<\/span><\/strong><\/h6>\n

\"\u0628\u0631\u0631\u0633\u06cc<\/p>\n

\u0634\u06a9\u0644-13: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u0628\u06cc-\u062a\u06cc-\u0633\u06cc-\u0627\u0633 \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0.45s.<\/span><\/strong><\/h6>\n

 <\/p>\n

<\/a>\u0631\u0648\u0634 \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 (Cranck-Nicolson)<\/strong><\/span><\/span><\/h4>\n

\u0631\u0648\u0634 \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 \u0628\u0647 \u0646\u062d\u0648\u06cc \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0631\u0648\u0634\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0648 \u0636\u0645\u0646\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0628\u06cc\u0634\u062a\u0631\u060c \u062a\u0648\u062c\u0647 \u0634\u0648\u062f \u06a9\u0647 \u062a\u0631\u0645 \u062f\u0648\u0645 \u0627\u0648\u0644\u06cc\u0646 \u0631\u0627\u0628\u0637\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (29) \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (33) \u0628\u0627\u0632 \u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (33)\u060c \u062a\u0631\u0645 \u062f\u0648\u0645 \u0627\u0648\u0644\u06cc\u0646 \u0631\u0627\u0628\u0637\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (29) \u0627\u0633\u062a \u0628\u062c\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06cc n+1 \u0628\u0627\u0634\u062f\u060c \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 \u0632\u0645\u0627\u0646\u06ccn+1\/2 \u00a0(\u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 n \u0648 n+1) \u0627\u0633\u062a. \u0641\u0631\u0645 \u0646\u0647\u0627\u06cc\u06cc \u0631\u0648\u0634 \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (34) \u0627\u0633\u062a.<\/span><\/p>\n

\"\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646<\/p>\n

\u0627\u06cc\u0646 \u0631\u0648\u0634 \u0627\u0632 \u062f\u0642\u062a \u0628\u0627\u0644\u0627 \u0648 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0628\u0633\u06cc\u0627\u0631 \u062e\u0648\u0628\u06cc (\u0628\u06cc \u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631) \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0628\u0648\u062f\u0647 \u0648 \u0628\u0637\u0648\u0631 \u06af\u0633\u062a\u0631\u062f\u0647 \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u062e\u0637\u0627\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0627\u0632 \u0646\u0648\u0639 \u0646\u0648\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0647\u0645\u0627\u0646\u0646\u062f \u0631\u0648\u0634 \u0642\u0628\u0644 \u06cc\u06a9 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647 \u0642\u0637\u0631\u06cc \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u062b\u0627\u0644 \u20131 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644\u0647\u0627\u06cc (14) \u0648 (15) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-14: \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646\u060c \u0627\u0644\u0641: C=0.45\u060c \u0628: C=0.9996.<\/span><\/strong><\/h6>\n

\"\u0628\u0631\u0631\u0633\u06cc<\/p>\n

\u0634\u06a9\u0644-15: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0.45 S.<\/span><\/strong><\/h6>\n

\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0627\u0632 \u0634\u06a9\u0644\u0647\u0627\u06cc (14) \u0648 (15) \u067e\u06cc\u062f\u0627\u0633\u062a\u060c \u062f\u0631 \u0631\u0648\u0634 \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 \u067e\u0627\u0633\u062e\u200c\u0647\u0627 \u062f\u0627\u0631\u0627\u06cc \u0646\u0648\u0633\u0627\u0646\u0627\u062a \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0632\u0645\u0627\u0646 \u0645\u06cc\u0632\u0627\u0646 \u062e\u0637\u0627 \u0646\u06cc\u0632 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0631\u0648\u0634 \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 \u0642\u0628\u0644 \u0627\u0632 \u0634\u0631\u0648\u0639 \u0645\u0648\u062c \u062f\u0627\u0645\u0646\u0647 \u0646\u0648\u0633\u0627\u0646 \u0635\u0641\u0631 \u0646\u0628\u0648\u062f\u0647 \u0648 \u0634\u0627\u0647\u062f \u0646\u0648\u0633\u0627\u0646\u0627\u062a \u0632\u06cc\u0627\u062f\u06cc \u067e\u06cc\u0634 \u0627\u0632 \u0634\u0631\u0648\u0639 \u062f\u0631 \u0634\u06a9\u0644 (14) \u0647\u0633\u062a\u06cc\u0645. \u0639\u0644\u062a \u0627\u06cc\u0646 \u0627\u0645\u0631 \u0646\u06cc\u0632 \u0648\u062c\u0648\u062f \u062a\u0631\u0645 un<\/sup>j-1<\/sub><\/em><\/strong> \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (33) \u0648 (34) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0646\u06a9\u062a\u0647 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0627\u06cc\u0646\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u0686\u0647 \u0647\u0631 \u0642\u062f\u0631 \u0645\u0642\u062f\u0627\u0631 \u0639\u062f\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0627\u0641\u0632\u0627\u06cc\u0634 \u06cc\u0627\u0628\u062f \u062f\u0631 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u062d\u0644 \u0645\u0633\u0626\u0644\u0647 \u062a\u0623\u062b\u06cc\u0631\u06cc \u0646\u062f\u0627\u0631\u062f\u060c \u0627\u0645\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0628\u06cc\u0634 \u0627\u0632 \u0627\u0646\u062f\u0627\u0632\u0647 \u0628\u0632\u0631\u06af \u0639\u062f\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u0648\u062c\u0628 \u06a9\u0627\u0647\u0634 \u062f\u0642\u062a \u062f\u0631 \u067e\u0627\u0633\u062e\u0647\u0627\u06cc \u0646\u0647\u0627\u06cc\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f (\u0634\u06a9\u064415).<\/span><\/p>\n

 <\/p>\n

\u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u0628\u0627 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/span><\/h2>\n

\u0627\u0633\u0627\u0633 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u0647\u0645\u0627\u0646\u0646\u062f \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0628\u0647\u062a\u0631 \u0627\u0632 \u0686\u06af\u0648\u0646\u06af\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645\u060c \u0645\u062b\u0627\u0644-2 \u0627\u0631\u0627\u0626\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u062d\u0644 \u0639\u062f\u062f\u06cc \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0628\u0627 \u0631\u0648\u0634 \u062c\u0647\u0634\u06cc \u0646\u0642\u0637\u0647 \u0645\u06cc\u0627\u0646\u06cc(Leapfrog Method) [4] \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\u0645\u062b\u0627\u0644-2:<\/strong><\/span><\/p>\n

\u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0632\u06cc\u0631 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u00a0\u0633\u0631\u0639\u062a \u0635\u0648\u062a \u0627\u0633\u062a (\u0645\u0639\u0627\u062f\u0644\u0647 35). \u0628\u0647 \u0645\u0646\u0638\u0648\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u062f\u0648 \u062f\u0633\u062a\u0647 \u0634\u0631\u0627\u0626\u0637 \u0627\u0648\u0644\u06cc\u0647 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0627\u06cc\u0646 \u0634\u0631\u0627\u0626\u0637 \u0628\u0647\u200c \u0635\u0648\u0631\u062a \u0631\u0648\u0627\u0628\u0637 (36) \u062a\u0639\u0631\u06cc\u0641 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc \u06a9\u0647 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u062f\u06cc\u0648\u0627\u0631\u0647 \u062c\u0627\u0645\u062f \u0645\u06cc\u200c\u0628\u0627\u0634\u062f \u062f\u0631 \u0642\u0627\u0644\u0628 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (37) \u062a\u0639\u06cc\u06cc\u0646 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u0645\u062b\u0627\u0644<\/p>\n

\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u062c\u0647\u0634\u06cc \u0646\u0642\u0637\u0647\u200c\u0627\u06cc \u0645\u06cc\u0627\u0646\u06cc\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0627 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u062f\u0631 \u0642\u0627\u0644\u0628 \u0645\u0639\u0627\u062f\u0644\u0647 (38) \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0633\u0647 \u0645\u0631\u062d\u0644\u0647\u200c\u0627\u06cc \u0627\u0633\u062a\u060c \u06cc\u0639\u0646\u06cc \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u062f\u0631 \u0645\u0631\u0627\u062d\u0644 \u0632\u0645\u0627\u0646\u06cc n<\/em><\/strong>\u060c n-1<\/em><\/strong> \u0648 n+1<\/em><\/strong> \u00a0<\/em><\/strong>\u0638\u0627\u0647\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u0628\u0631\u0627\u06cc \u0634\u0631\u0648\u0639 \u0631\u0648\u0646\u062f \u062d\u0644 \u0628\u0647 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0634\u0631\u0648\u0639 \u06a9\u0646\u0646\u062f\u0647 \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a. \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0634\u0631\u0648\u0639 \u06a9\u0646\u0646\u062f\u0647 \u0627\u0632 \u062f\u0648\u0645\u06cc\u0646 \u0634\u0631\u0637 \u0627\u0648\u0644\u06cc\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f(\u0645\u0639\u0627\u062f\u0644\u0647 39). \u0628\u0627 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 (39) \u062f\u0631 \u0631\u0627\u0628\u0637\u0647\u200c\u06cc \u062f\u0648\u0645\u00a0 \u0645\u0639\u0627\u062f\u0644\u0647 (38) \u0645\u0639\u0627\u062f\u0644\u0647 (40) \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u060c \u0645\u0639\u0627\u062f\u0644\u0647 (40) \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0634\u0631\u0648\u0639 \u06a9\u0646\u0646\u062f\u0647 \u0627\u0633\u062a \u0648 \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062a\u0646\u0647\u0627 \u0628\u0631\u0627\u06cc \u06af\u0627\u0645 \u0632\u0645\u0627\u0646\u06cc \u0627\u0648\u0644 \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f (\u0645\u0639\u0627\u062f\u0644\u0647 41).<\/span><\/p>\n

\"\u06af\u0633\u0633\u062a\u0647<\/p>\n

\u0628\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 u2<\/sup>i<\/sub><\/em><\/strong> \u062f\u0631 \u062a\u0645\u0627\u0645 \u0647\u0627\u060c \u062f\u0648 \u062f\u0633\u062a\u0647 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u062f\u0631 n=1<\/em><\/strong> \u0648 n=2<\/em><\/strong> \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a \u06a9\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0622\u0646\u0647\u0627 \u0648 \u0645\u0639\u0627\u062f\u0644\u0647 (38) \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u062e\u0637\u06cc \u0627\u0645\u06a9\u0627\u0646\u200c\u067e\u0630\u06cc\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0646\u062a\u0627\u06cc\u062c \u0645\u0631\u0628\u0648\u0637\u0647 \u062f\u0631 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (16) \u0648 (17) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0645\u0648\u062c \u0627\u0648\u0644\u06cc\u0647 \u0628\u0647 \u062f\u0648 \u0645\u0648\u062c (\u0647\u0631\u06a9\u062f\u0627\u0645 \u0628\u0627 \u062f\u0627\u0645\u0646\u0647\u200c\u0647\u0627\u06cc \u0628\u0631\u0627\u0628\u0631 \u0646\u0635\u0641 \u062f\u0627\u0645\u0646\u0647 \u0645\u0648\u062c \u0627\u0648\u0644\u06cc\u0647) \u0628\u0627 \u0637\u0648\u0644 \u0645\u0648\u062c\u200c\u0647\u0627\u06cc \u0645\u0633\u0627\u0648\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u062f\u0631 \u062f\u0648\u062c\u0647\u062a \u0645\u0634\u062e\u0635\u0647 \u067e\u06cc\u0634\u0631\u0648\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0627\u0645\u0648\u0627\u062c \u0631\u0648\u06cc \u062f\u06cc\u0648\u0627\u0631\u0647 \u0645\u0646\u0639\u06a9\u0633 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0639\u0644\u0627\u0645\u062a u<\/em><\/strong> \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u0628\u0631\u0627\u06cc \u0631\u0648\u0634\u0646 \u0628\u0648\u062f\u0646 \u0634\u06a9\u0644\u060c \u0647\u0645\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0646\u0641\u06cc u<\/em><\/strong> \u062f\u0631 \u0634\u06a9\u0644 \u062a\u063a\u06cc\u06cc\u0631 \u0639\u0644\u0627\u0645\u062a \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0648 \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u062b\u0628\u062a \u0631\u0633\u0645 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0628\u0631\u0627\u06cc C=1<\/em><\/strong> \u062c\u0648\u0627\u0628 \u062f\u0642\u06cc\u0642 \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f. \u0627\u0632 \u0637\u0631\u0641\u06cc \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u0645\u0633\u0626\u0644\u0647 \u0641\u0648\u0642 \u062f\u0627\u0631\u0627\u06cc \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u0628\u0631\u0627\u06cc C<1<\/em><\/strong> \u00a0\u0634\u0627\u0647\u062f \u0628\u0631\u0648\u0632 \u062e\u0637\u0627\u06cc \u0646\u0648\u0633\u0627\u0646\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u06cc\u0645 (\u0634\u06a9\u0644\u200c\u0647\u0627\u06cc 16 \u0627\u0644\u0641 \u0648 17).<\/span><\/p>\n

\"\u062d\u0644<\/p>\n

\u0634\u06a9\u0644-16: \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u062c\u0647\u0634\u06cc \u0646\u0642\u0637\u0647 \u0645\u06cc\u0627\u0646\u06cc\u060c \u0627\u0644\u0641: C=0.45\u060c \u0628: C=0.9996.<\/strong><\/span><\/h6>\n

 <\/p>\n

\"\u0628\u0631\u0631\u0633\u06cc<\/p>\n

\u0634\u06a9\u0644-17: \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646 \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u06a9\u0648\u0631\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0632\u0645\u0627\u0646 t=0.28 S.<\/span><\/strong><\/h6>\n

 <\/p>\n

-[1]<\/strong><\/span><\/p>\n

K. A. Hoffman AND S.T. Chaing, \u201cComputational Fluid Dynamics for Engineer\u201d, Volume 1, Engineering Education System, Wichita, Kansas, 1993<\/strong><\/span><\/p>\n

 <\/p>\n

\u0628\u0627\u0632\u06af\u0634\u062a<\/strong><\/a><\/span><\/h3>\n
\n

\u0645\u0637\u0627\u0644\u0628 \u0645\u0631\u062a\u0628\u0637<\/strong><\/h3>\n
\n

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\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc (\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0644\u0627\u067e\u0644\u0627\u0633 \u0648 \u067e\u0648\u0622\u0633\u0648\u0646) \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/a><\/strong><\/span><\/h4>\n

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc (\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0646\u062a\u0642\u0627\u0644 \u06af\u0631\u0645\u0627) \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/span><\/strong><\/a><\/h4>\n

\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc<\/strong><\/span><\/a><\/h4>\n

\u0628\u0631\u0627\u06cc \u06a9\u0633\u0628 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0628\u0627 \u0645\u0627 \u062a\u0645\u0627\u0633 \u0628\u06af\u06cc\u0631\u06cc\u062f<\/strong><\/a><\/em><\/span><\/h4>\n
\u062f\u06a9\u062a\u0631 \u0645\u062d\u0645\u062f \u0637\u06cc\u0628\u06cc \u0631\u0647\u0646\u06cc<\/strong><\/em><\/a><\/span><\/h5>\n
\u0645\u062d\u0645\u062f\u0631\u0636\u0627 \u06a9\u0644\u06cc\u0686<\/a><\/em><\/strong><\/span><\/h5>\n

<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f Solving Hyperbolic PDEs Using FDM \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u062f\u0631 \u0627\u06cc\u0646 \u067e\u0633\u062a \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0639\u0631\u0648\u0641\u200c\u062a\u0631\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0628\u0647 \u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f. \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631… Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":11569,"parent":3477,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-11522","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\n\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f - cfd-mrk<\/title>\n<meta name=\"description\" content=\"\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u062f\u0631 \u0627\u06cc\u0646 \u067e\u0633\u062a \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c 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