{"id":11998,"date":"2021-11-28T08:20:45","date_gmt":"2021-11-28T04:50:45","guid":{"rendered":"https:\/\/cfd-mrk.ir\/?page_id=11998"},"modified":"2021-11-28T09:11:20","modified_gmt":"2021-11-28T05:41:20","slug":"solving-parabolic-pdes-using-fdm","status":"publish","type":"page","link":"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/solving-parabolic-pdes-using-fdm\/","title":{"rendered":"\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\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 \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/h2>\n

Solving Parabolic <\/strong>PDEs Using FDM<\/strong><\/h2>\n

\u0628\u0645\u0646\u0638\u0648\u0631 \u0628\u0631\u0631\u0633\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u06cc\u06a9 \u0648 \u062f\u0648 \u0628\u0639\u062f\u06cc \u06af\u0631\u0645\u0627 \u0645\u062f \u0646\u0638\u0631 \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062a\u0639\u062f\u062f\u06cc \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0628\u0631\u0627\u06cc \u0641\u0636\u0627\u0647\u0627\u06cc\u06cc \u06cc\u06a9 \u0628\u0639\u062f\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 1<\/span><\/strong><\/a>\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 17) \u0648 \u062f\u0648 \u0628\u0639\u062f\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 28) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0648 \u0636\u0645\u0646\u06cc \u062a\u0642\u0633\u06cc\u0645\u200c\u0628\u0646\u062f\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0634\u062a\u0627\u0631\u060c \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u0630\u06a9\u0648\u0631 \u0628\u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/span><\/p>\n

 <\/p>\n

\u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0633\u0647\u0645\u0648\u06cc \u06cc\u06a9 \u0628\u0639\u062f\u06cc<\/strong><\/span><\/h2>\n
\u0645\u062b\u0627\u0644-1: \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0647\u062f\u0627\u06cc\u062a \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u062f\u0631 \u0637\u0648\u0644 \u06cc\u06a9 \u0628\u0627\u0631\u06cc\u06a9\u0647 (Slab)\u00a0<\/strong><\/span><\/h6>\n

\u0628\u0639\u0646\u0648\u0627\u0646 \u0627\u0648\u0644\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0647\u062f\u0627\u06cc\u062a \u062f\u0631 \u0637\u0648\u0644 \u06cc\u06a9 \u0628\u0627\u0631\u06cc\u06a9\u0647 (Slab) \u0628\u0647 \u0637\u0648\u0644 0.3 \u0645\u062a\u0631 \u06a9\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0645\u062f\u0644\u0633\u0627\u0632\u06cc \u0634\u062f\u0647 (\u0645\u0639\u0627\u062f\u0644\u0647 17) \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f. \u0647\u062f\u0641 \u0627\u0632 \u062d\u0644 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 \u062a\u0639\u06cc\u06cc\u0646 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627\u06cc\u06cc \u0631\u0648\u06cc \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0639\u062f\u062f\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

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

<\/h3>\n

\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d (Explicit Methods) \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u062f\u0631 \u06cc\u06a9 \u0628\u0639\u062f<\/strong><\/span><\/h3>\n

\u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f\u060c <\/span>\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 \u062a\u0648\u0632\u06cc\u0639 \u06af\u0631\u0645\u0627 (\u0645\u0639\u0627\u062f\u0644\u0647 17) \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0634\u062f\u0647 \u06a9\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc\u06cc \u0646\u0638\u06cc\u0631 \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646\u060c \u0631\u06cc\u0686\u0627\u0631\u062f\u0633\u0648\u0646 \u0648 \u062f\u0648\u0641\u0648\u0631\u062a-\u0641\u0631\u0627\u0646\u06a9\u0644 \u0627\u0632 \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0628\u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647\u060c \u0627\u06cc\u0646 \u0631\u0648\u0634\u0647\u0627 \u0628\u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f.<\/span><\/p>\n

\u0631\u0648\u0634 \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646<\/strong><\/span><\/h4>\n

\u062f\u0631 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646 (FTCS) \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (18) \u0646\u0648\u0634\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (19) \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 [(\u2206t) \u0648 2<\/sup>(\u2206x)]<\/em> \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. <\/span>\u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u062f\u0631\u06af\u06cc\u0631 \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644 (1) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062c\u0648\u0627\u0628\u200c\u0647\u0627\u06cc \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644-1 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (2) \u0648 (3) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647\u00a0 \u0627\u0633\u062a.<\/span><\/p>\n

\"<\/p>\n

\u0634\u06a9\u0644-1: \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u062f\u0631\u06af\u06cc\u0631 \u062f\u0631 \u0631\u0648\u0634 \u0635\u0631\u06cc\u062d \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646.<\/span><\/strong><\/h5>\n

 <\/p>\n

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

\u0634\u06a9\u0644-2: \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u06cc\u06a9 \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc \u0627\u0644\u0641: 5 \u062b\u0627\u0646\u06cc\u0647\u060c \u0628: 30 \u062b\u0627\u0646\u06cc\u0647 \u0648 \u062c: 60 \u062b\u0627\u0646\u06cc\u0647 (\u0631\u0648\u0634 FTCS).<\/strong><\/span><\/h5>\n

\u0646\u062a\u0627\u06cc\u062c \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0634\u06a9\u0644 \u0641\u0648\u0642 \u062d\u0627\u06a9\u06cc \u0627\u0632 \u062a\u0637\u0627\u0628\u0642 \u062f\u0642\u06cc\u0642 \u0646\u062a\u0627\u06cc\u062c \u0639\u062f\u062f\u06cc \u0648 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0634\u06a9\u0644 (2-\u0627\u0644\u0641) \u067e\u06cc\u062f\u0627\u0633\u062a \u0637\u0648\u0644 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0627\u0632 \u0628\u0627\u0631\u06cc\u06a9\u0647 300 \u062f\u0631\u062c\u0647 \u06a9\u0644\u0648\u06cc\u0646 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0647\u0645 \u0628\u062e\u0627\u0637\u0631 \u062f\u0645\u0627\u06cc \u0627\u0648\u0644\u06cc\u0647 (\u0634\u0631\u0637 \u0627\u0648\u0644\u06cc\u0647) \u0628\u0627\u0631\u06cc\u06a9\u0647 \u0627\u0633\u062a. \u0628\u0627 \u06af\u0630\u0634\u062a \u0632\u0645\u0627\u0646\u060c \u062f\u0645\u0627 \u062f\u0631 \u0637\u0648\u0644 \u0645\u06cc\u0644\u0647 \u0627\u0641\u0632\u0627\u06cc\u0634 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0647 (\u0634\u06a9\u0644\u200c\u0647\u0627\u06cc 2-\u0628 \u0648 \u062c) \u062a\u0627 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0628\u0647 \u062d\u0627\u0644\u062a \u062a\u0639\u0627\u062f\u0644 \u0628\u0631\u0633\u062f \u06a9\u0647 \u06cc\u06a9 \u062a\u0648\u0632\u06cc\u0639 \u062e\u0637\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f (\u0634\u06a9\u0644 3). \u0637\u0628\u06cc\u0639\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0627 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u0645\u0627\u062f\u0647 \u0628\u0627\u0631\u06cc\u06a9\u0647\u060c \u0632\u0645\u0627\u0646 \u0628\u0647 \u062a\u0639\u0627\u062f\u0644 \u0631\u0633\u06cc\u062f\u0646 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0622\u0646 \u0646\u06cc\u0632 \u062a\u063a\u06cc\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u06cc\u0627\u0641\u062a. \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0636\u0631\u06cc\u0628 \u0647\u062f\u0627\u06cc\u062a \u062d\u0631\u0627\u0631\u062a\u06cc \u0645\u0627\u062f\u0647\u060c \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646 \u06a9\u0645\u062a\u0631\u06cc \u0628\u0647 \u062f\u0645\u0627\u06cc \u062a\u0639\u0627\u062f\u0644 \u0645\u06cc\u200c\u0631\u0633\u062f.<\/span><\/p>\n

 <\/p>\n

\"\u062a\u0648\u0632\u06cc\u0639<\/p>\n

\u0634\u06a9\u0644-3: \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627\u06cc \u062a\u0639\u0627\u062f\u0644 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u06cc\u06a9 \u0628\u0627\u0631\u06cc\u06a9\u0647 (\u062f\u0631 \u0632\u0645\u0627\u0646 180 \u062b\u0627\u0646\u06cc\u0647).<\/span><\/strong><\/h5>\n

 <\/p>\n

\u0631\u0648\u0634 \u0631\u06cc\u0686\u0627\u0631\u062f\u0633\u0648\u0646 (Richardson Method)<\/strong><\/span><\/h4>\n

\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062a\u0642\u0631\u06cc\u0628 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u0647\u0645 \u0628\u0631\u0627\u06cc \u0632\u0645\u0627\u0646 \u0648 \u0647\u0645 \u0628\u0631\u0627\u06cc \u0645\u06a9\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0631\u0627\u0628\u0637\u0647 \u062c\u0628\u0631\u06cc \u067e\u06cc\u0634\u0646\u0647\u0627\u062f\u06cc \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (19) \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 [(\u2206t) 2<\/sup>, (\u2206x)2<\/sup>]<\/em> \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0627\u0633\u062a. \u0622\u0646\u0627\u0644\u06cc\u0632 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u06cc\u200c\u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631 \u0628\u0648\u062f\u0647 \u0648 \u0627\u0632 \u0647\u06cc\u0686 \u0645\u0642\u062f\u0627\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0645\u0646\u0627\u0633\u0628\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0646\u06cc\u0633\u062a. \u0646\u0645\u0648\u0646\u0647\u200c\u0627\u06cc \u0627\u0632 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644 (4) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u06a9\u0647 \u0646\u0627\u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u062d\u0644 \u0628\u0635\u0648\u0631\u062a \u0646\u0648\u0633\u0627\u0646\u0627\u062a \u0634\u062f\u06cc\u062f \u062f\u0631 \u067e\u0627\u0633\u062e\u200c\u0647\u0627 \u0645\u0634\u062e\u0635 \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u062f\u0631 \u062d\u0627\u0644\u062a \u06a9\u0644\u06cc \u0631\u0648\u0634 \u0631\u06cc\u0686\u0627\u0631\u062f\u0633\u0648\u0646 \u0628\u0647 \u062a\u0646\u0647\u0627\u06cc\u06cc \u0647\u06cc\u0686 \u06a9\u0627\u0631\u0628\u0631\u062f\u06cc \u062f\u0631 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc \u0646\u062f\u0627\u0631\u062f.<\/span><\/p>\n

 <\/p>\n

\"\u0631\u0648\u0634<\/p>\n

\u0634\u06a9\u0644-4: \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646 5 \u062b\u0627\u0646\u06cc\u0647 (\u0631\u0648\u0634 \u0631\u06cc\u0686\u0627\u0631\u062f\u0633\u0648\u0646).<\/strong><\/span><\/p>\n

\u00a0<\/strong><\/span><\/p>\n

\u0631\u0648\u0634 \u062f\u0648\u0641\u0648\u0631\u062a-\u0641\u0631\u0627\u0646\u06a9\u0644 (DuFort-Frankel Scheme)<\/strong><\/span><\/h4>\n

\u062f\u0631 \u0631\u0648\u0634 \u062f\u0648\u0641\u0648\u0631\u062a-\u0641\u0631\u0627\u0646\u06a9\u0644 \u0646\u06cc\u0632 \u0647\u0645\u0627\u0646\u0646\u062f \u0631\u0648\u0634 \u0631\u06cc\u0686\u0627\u0631\u062f\u0633\u0648\u0646 \u0627\u0632 \u062a\u0642\u0631\u06cc\u0628 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u0628\u0631\u0627\u06cc \u0632\u0645\u0627\u0646 \u0648 \u0645\u06a9\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0627 \u0627\u06cc\u0646 \u062a\u0641\u0627\u0648\u062a \u06a9\u0647 \u0628\u062c\u0627\u06cc un<\/sup>i<\/sub><\/em>\u00a0 \u062f\u0631 \u0631\u0648\u0634 \u0631\u06cc\u0686\u0627\u0631\u062f\u0633\u0648\u0646 \u0627\u0632 \u0645\u0642\u062f\u0627\u0631 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 un+1<\/sup>i<\/sub><\/em> \u0648 un-1<\/sup>i<\/sub><\/em> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0639\u0644\u062a \u0627\u06cc\u0646 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u0628\u0647 \u062e\u0627\u0637\u0631 \u0645\u0644\u0627\u062d\u0638\u0627\u062a \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0627\u0633\u062a. \u062f\u0631 \u0648\u0627\u0642\u0639\u060c \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0647\u0645\u0627\u0646 \u0631\u0648\u0634 \u062a\u0635\u062d\u06cc\u062d \u0634\u062f\u0647 \u0631\u06cc\u0686\u0627\u0631\u062f\u0633\u0648\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u06a9\u0644\u06cc \u0622\u0646 \u0628\u0635\u0648\u0631\u062a \u0631\u0627\u0628\u0637\u0647 (20) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0630\u06a9\u0648\u0631 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0641\u0631\u0645 \u0645\u0639\u0627\u062f\u0644\u0647 (21) \u0646\u06cc\u0632 \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u0628\u0627 \u0645\u0631\u062a\u0628 \u06a9\u0631\u062f\u0646 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647\u060c \u0641\u0631\u0645 \u0646\u0647\u0627\u06cc\u06cc \u0631\u0648\u0634 \u062f\u0648\u0641\u0648\u0631\u062a-\u0641\u0631\u0627\u0646\u06a9\u0644 \u062f\u0631 \u0642\u0627\u0644\u0628 \u0645\u0639\u0627\u062f\u0644\u0647 (22) \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

\"<\/p>\n

\u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644 (5) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

\"\u062a\u0648\u0632\u06cc\u0639<\/p>\n

\u0634\u06a9\u0644-5: \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u06cc\u06a9 \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc \u0627\u0644\u0641: 5 \u062b\u0627\u0646\u06cc\u0647\u060c \u0628: 30 \u062b\u0627\u0646\u06cc\u0647 \u0648 \u062c: 60 \u062b\u0627\u0646\u06cc\u0647 (\u0631\u0648\u0634 \u062f\u0648\u0641\u0648\u0631\u062a-\u0641\u0631\u0627\u0646\u06a9\u0644).<\/strong><\/h5>\n

\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0631\u0648\u0634 \u0645\u0630\u06a9\u0648\u0631 \u0644\u0627\u0632\u0645\u0633\u062a \u062f\u0631 \u0634\u0631\u0648\u0639 \u0627\u0646\u062c\u0627\u0645 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u060c \u0645\u0642\u062f\u0627\u0631 ui<\/sub><\/em> \u062f\u0631 \u06af\u0627\u0645\u200c\u0647\u0627\u06cc \u0632\u0645\u0627\u0646\u06cc n \u0648 n-1 \u0645\u0639\u0644\u0648\u0645 \u0628\u0627\u0634\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u06cc\u0627 \u062f\u0648 \u0645\u0631\u062d\u0644\u0647 \u0632\u0645\u0627\u0646\u06cc \u0627\u0632 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0628\u0627\u06cc\u062f \u0645\u0648\u062c\u0648\u062f \u0628\u0627\u0634\u062f \u0648 \u06cc\u0627 \u0627\u06cc\u0646\u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644\u062a\u0647\u0627\u06cc \u062e\u0627\u0635 (\u0645\u0627\u0646\u0646\u062f \u0627\u0648\u0644\u06cc\u0646 \u06af\u0627\u0645 \u0632\u0645\u0627\u0646\u06cc\u060c n+1=1) \u0634\u0631\u0648\u0639 \u0634\u062f\u0647 \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc ui<\/sub><\/em> \u062f\u0631 \u06af\u0627\u0645\u0647\u0627\u06cc \u0632\u0645\u0627\u0646\u06cc n \u0648 n-1 \u0647\u0645\u0627\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062a\u0639\u06cc\u06cc\u0646 \u0634\u062f\u0647 \u0634\u0631\u0637 \u0627\u0648\u0644\u06cc\u0647 \u0628\u0627\u0634\u062f. \u062f\u0631 \u0631\u0648\u0634 \u062f\u0648\u0641\u0648\u0631\u062a-\u0641\u0631\u0627\u0646\u06a9\u0644 \u062f\u0648 \u0646\u06a9\u062a\u0647 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0627\u0633\u062a. \u0627\u0648\u0644 \u0627\u06cc\u0646\u06a9\u0647 \u062f\u0642\u062a \u062d\u0644 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0647 \u062d\u062f\u0633 \u0627\u0648\u0644\u06cc\u0647 \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a. \u062f\u0648\u0645 \u0627\u06cc\u0646\u06a9\u0647\u060c \u0627\u0632 \u0622\u0646\u062c\u0627\u0626\u06cc\u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0646\u062a\u0627\u06cc\u062c\u060c \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u062f\u0631 \u062f\u0648 \u06af\u0627\u0645 \u0632\u0645\u0627\u0646\u06cc \u0642\u0628\u0644\u06cc \u0646\u06cc\u0632 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a\u060c \u0644\u0630\u0627 \u062d\u0627\u0641\u0638\u0647 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0633\u0627\u06cc\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/span><\/p>\n

<\/h3>\n

\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc <\/strong><\/span>\u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u062f\u0631 \u06cc\u06a9 \u0628\u0639\u062f<\/strong><\/span><\/h3>\n

\u0631\u0648\u0634 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062c\u0628\u0631\u06cc \u0646\u0627\u0634\u06cc \u0627\u0632 \u06af\u0633\u0633\u062a\u0647 \u0633\u0627\u0632\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u06cc\u06a9 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0628\u0647 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u0645\u0639\u0631\u0648\u0641 \u0627\u0633\u062a. \u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc\u060c \u0627\u06af\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (17) \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (23) \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0634\u0648\u062f\u060c \u0622\u0646 \u0631\u0627 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u06af\u0648\u06cc\u0646\u062f.<\/span><\/p>\n

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

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

 <\/p>\n

\u0631\u0648\u0634 \u0644\u0627\u0633\u0648\u0646\u0646 (Laasonen Method)<\/strong><\/span><\/h4>\n

\u0631\u0648\u0634 \u0644\u0627\u0633\u0648\u0646\u0646 \u0633\u0627\u062f\u0647\u200c\u062a\u0631\u06cc\u0646 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0622\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (23) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u06af\u06cc\u0631 \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0628\u0627 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644 (6) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0627 \u0628\u06a9\u0627\u0631\u06af\u06cc\u0631\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0641\u0648\u0642 \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645\u06cc \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0634\u0628\u06a9\u0647\u060c \u06cc\u06a9 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062c\u0628\u0631\u06cc \u062e\u0637\u06cc \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0686\u06af\u0648\u0646\u06af\u06cc \u062d\u0644 \u0627\u06cc\u0646 \u062f\u0633\u062a\u06af\u0627\u0647 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627<\/span> <\/strong><\/a>\u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u062d\u0644 \u0645\u062b\u0627\u0644-1 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644 (7) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u06a9\u0647 \u0647\u0645\u062e\u0648\u0627\u0646\u06cc \u0628\u0633\u06cc\u0627\u0631 \u062e\u0648\u0628\u06cc \u0631\u0627 \u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627 \u0646\u062a\u0627\u06cc\u062c \u062f\u0642\u06cc\u0642 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/span><\/p>\n

 <\/p>\n

\"\u0646\u0648\u062f\u0647\u0627\u06cc<\/span><\/p>\n

\u0634\u06a9\u0644-6: \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u062f\u0631\u06af\u06cc\u0631 \u062f\u0631 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u0644\u0627\u0633\u0648\u0646\u0646.<\/strong><\/span><\/h5>\n

\u00a0<\/strong><\/span><\/p>\n

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

\u0634\u06a9\u0644-7: \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u06cc\u06a9 \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc \u0627\u0644\u0641: 5 \u062b\u0627\u0646\u06cc\u0647\u060c \u0628: 30 \u062b\u0627\u0646\u06cc\u0647 \u0648 \u062c: 60 \u062b\u0627\u0646\u06cc\u0647 (\u0631\u0648\u0634 \u0644\u0627\u0633\u0648\u0646\u0646).<\/strong><\/span><\/p>\n

\u00a0<\/strong><\/span><\/p>\n

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

\u0627\u06af\u0631 \u062f\u0631 \u0631\u0648\u0634 \u0644\u0627\u0633\u0648\u0646\u0646\u060c \u062a\u0631\u0645 \u0627\u0646\u062a\u0634\u0627\u0631 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (23) \u0628\u0627 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc n \u0648 n+1 \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0634\u0648\u062f\u060c \u0641\u0631\u0645 \u06af\u0633\u0633\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0630\u06a9\u0648\u0631 \u0628\u0647 \u0631\u0627\u0628\u0637\u0647 (24) \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0634\u0628\u06a9\u0647 \u062f\u0631 \u0634\u06a9\u0644 (8)\u060c \u0633\u0645\u062a \u0686\u067e \u0645\u0639\u0627\u062f\u0644\u0647 (24) \u0628\u06cc\u0627\u0646\u06af\u0631 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u0628\u0631\u0627\u06cc \u06af\u0631\u0647 A \u0627\u0633\u062a. \u062f\u0631\u062d\u0627\u0644\u06cc\u06a9\u0647\u060c \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u062a\u0631\u0645 \u0627\u0646\u062a\u0634\u0627\u0631 \u062f\u0631 \u0647\u0645\u0627\u0646 \u06af\u0631\u0647 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631 \u0642\u0627\u0644\u0628 \u062f\u0648 \u0645\u0631\u062d\u0644\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0648 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a (25) \u0648 (26) \u0646\u0648\u0634\u062a. \u0645\u0639\u0627\u062f\u0644\u0647 (25) \u0628\u0635\u0648\u0631\u062a \u0635\u0631\u06cc\u062d \u0648 \u0645\u0639\u0627\u062f\u0644\u0647 (26) \u0628\u0635\u0648\u0631\u062a \u0636\u0645\u0646\u06cc \u0642\u0627\u0628\u0644 \u062d\u0644 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

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

\"\u0686\u06cc\u062f\u0647<\/p>\n

\u0634\u06a9\u0644-8: \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u06af\u06cc\u0631 \u062f\u0631 \u0631\u0648\u0634 \u0636\u0645\u0646\u06cc \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646.<\/strong><\/span><\/h5>\n

\u0628\u0627 \u062c\u0645\u0639 \u06a9\u0631\u062f\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (5-25) \u0648 (5-26) \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0647\u0645\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (5-24) \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 [2<\/sup>(t\u2206) \u0648 2<\/sup>(x\u2206)] <\/em>\u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0631\u0648\u0634 \u0645\u0630\u06a9\u0648\u0631 \u0628\u06cc\u200c\u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a \u0648 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a\u06cc \u062f\u0631 \u0645\u0642\u062f\u0627\u0631 \u06af\u0627\u0645 \u0632\u0645\u0627\u0646\u06cc\u060c t\u2206<\/em>\u060c \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f. \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631\u0634\u06a9\u0644 (9) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u06a9\u0647 \u0647\u0645\u062e\u0648\u0627\u0646\u06cc \u0628\u0633\u06cc\u0627\u0631 \u062e\u0648\u0628\u06cc \u0631\u0627 \u0628\u0627 \u0646\u062a\u0627\u06cc\u062c \u062f\u0642\u06cc\u0642 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/span><\/p>\n

 <\/p>\n

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

\u0634\u06a9\u0644-9: \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u06cc\u06a9 \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc \u0627\u0644\u0641: 5 \u062b\u0627\u0646\u06cc\u0647\u060c \u0628: 30 \u062b\u0627\u0646\u06cc\u0647 \u0648 \u062c: 60 \u062b\u0627\u0646\u06cc\u0647 (\u0631\u0648\u0634 \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646).<\/strong><\/h5>\n

 <\/p>\n

\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0647\u06cc\u0628\u0631\u06cc\u062f\u06cc \u0628\u062a\u0627<\/strong><\/span><\/h3>\n

\u0645\u0639\u0627\u062f\u0644\u0647 (17)\u00a0 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u06a9\u0644\u06cc \u0632\u06cc\u0631 \u06a9\u0647 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0648 \u0636\u0645\u0646\u06cc \u0627\u0633\u062a \u0648 \u0628\u0647 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0628\u062a\u06271<\/a> \u0645\u0639\u0631\u0648\u0641 \u0627\u0633\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u06af\u0633\u0633\u062a\u0647 \u0634\u0648\u062f:<\/span><\/p>\n

 <\/p>\n

\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f \u06a9\u0647 \u0628\u0631\u0627\u06cc 1\/2 \u2264 \u03b2 \u2264 1<\/em>\u060c \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u06cc \u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646 \u062f\u0631 \u062d\u0627\u0644\u062a\u200c\u0647\u0627\u06cc\u060c \u03b2 = 1\/2<\/em> \u0631\u0648\u0634 \u0645\u0630\u06a9\u0648\u0631 \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634 \u06a9\u0631\u0646\u06a9-\u0646\u06cc\u06a9\u0644\u0633\u0648\u0646\u060c \u03b2 = 1<\/em> \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634 \u0644\u0627\u0633\u0648\u0646\u0646\u060c 0 \u2264\u03b2 \u0648 \u03b2 \u2264 1\/2<\/em> \u0628\u0637\u0648\u0631 \u0645\u0634\u0631\u0648\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u03b2 = 0<\/em> \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634 FTCS\u00a0 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.\u00a0 \u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644 (10) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u06a9\u0647 \u0647\u0645\u062e\u0648\u0627\u0646\u06cc \u0628\u0633\u06cc\u0627\u0631 \u062e\u0648\u0628\u06cc \u0631\u0627 \u0628\u0627 \u0646\u062a\u0627\u06cc\u062c \u062f\u0642\u06cc\u0642 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/span><\/p>\n

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

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

\u0634\u06a9\u0644-10: \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u0628\u0627\u0631\u06cc\u06a9\u0647 \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc \u0627\u0644\u0641: 5 \u062b\u0627\u0646\u06cc\u0647\u060c \u0628: 30 \u062b\u0627\u0646\u06cc\u0647 \u0648 \u062c: 60 \u062b\u0627\u0646\u06cc\u0647 (\u0631\u0648\u0634 \u0628\u062a\u0627\u060c ).<\/strong><\/span><\/h5>\n

 <\/p>\n

\u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0633\u0647\u0645\u0648\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc<\/strong><\/span><\/h2>\n

\u0628\u0631\u0627\u06cc \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc \u062f\u0631 \u0641\u0636\u0627\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc\u060c \u062a\u0648\u0632\u06cc\u0639 \u0646\u0627\u067e\u0627\u06cc\u0627\u06cc \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0647\u062f\u0627\u06cc\u062a \u062f\u0631 \u06cc\u06a9 \u0635\u0641\u062d\u0647 \u062a\u062e\u062a \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a. \u0641\u0631\u0645 \u06a9\u0644\u06cc \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0647\u062f\u0627\u06cc\u062a \u062f\u0648 \u0628\u0639\u062f\u06cc \u0646\u0627\u067e\u0627\u06cc\u0627 (\u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc) \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (28) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

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

\u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0641\u0648\u0642\u060c\u03b1<\/em> \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u062b\u0627\u0628\u062a \u0627\u0633\u062a. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647\u060c \u062f\u0648 \u0631\u0648\u0634 FTCS \u0648 ADI \u0628\u0631\u0627\u06cc \u062d\u0644 \u0639\u062f\u062f\u06cc \u0627\u06cc\u0646 \u0646\u0648\u0639 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a (\u0645\u062b\u0627\u0644-2).<\/span><\/p>\n

\u0645\u062b\u0627\u0644-2: <\/strong><\/span>\u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0647\u062f\u0627\u06cc\u062a \u062f\u0648 \u0628\u0639\u062f\u06cc \u0631\u0648\u06cc \u06cc\u06a9 \u0635\u0641\u062d\u0647<\/strong><\/span><\/p>\n

\u062f\u0631 \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u0647\u062f\u0641 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u062d\u0627\u0644\u062a \u0646\u0627\u067e\u0627\u06cc\u0627 \u0631\u0648\u06cc \u06cc\u06a9 \u0635\u0641\u062d\u0647 \u0686\u0647\u0627\u0631 \u0636\u0644\u0639\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0627\u0628\u0639\u0627\u062f \u0635\u0641\u062d\u0647 \u0645\u0630\u06a9\u0648\u0631 1 \u0645\u062a\u0631 \u062f\u0631 \u062c\u0647\u062a X \u0648 2 \u0645\u062a\u0631 \u062f\u0631 \u062c\u0647\u062a Y \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a (\u0634\u06a9\u064411). \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc \u0627\u0639\u0645\u0627\u0644\u06cc \u0631\u0648\u06cc \u0633\u0637\u062d \u0645\u0630\u06a9\u0648\u0631 \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/span><\/p>\n

\"\u0634\u0631\u0637<\/span><\/p>\n

\u0627\u06cc\u0646 \u0635\u0641\u062d\u0647 \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u062f\u0645\u0627\u06cc \u0627\u0648\u0644\u06cc\u0647 300 \u062f\u0631\u062c\u0647 \u06a9\u0644\u0648\u06cc\u0646 \u0627\u0633\u062a\u060c \u062f\u0631 \u06cc\u06a9 \u0644\u062d\u0638\u0647 \u0636\u0644\u0639 \u067e\u0627\u06cc\u06cc\u0646\u06cc \u0622\u0646 \u062f\u0631 \u0645\u062d\u06cc\u0637\u06cc \u0628\u0627 \u062f\u0645\u0627\u06cc \u0645\u062a\u0641\u0627\u0648\u062a 400 \u062f\u0631\u062c\u0647 \u06a9\u0644\u0648\u06cc\u0646 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u0647\u062f\u0641 \u0645\u062d\u0627\u0633\u0628\u0647 \u067e\u0631\u0648\u0641\u06cc\u0644 \u062f\u0645\u0627 \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc 5\u060c 30 \u0648 90 \u062b\u0627\u0646\u06cc\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

\"\u0634\u0631\u0637<\/p>\n

\u0634\u06a9\u0644 11: \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc \u0645\u062b\u0627\u0644 2.<\/span><\/strong><\/h5>\n

 <\/p>\n

\u0631\u0648\u0634 \u0635\u0631\u06cc\u062d \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646<\/strong><\/span><\/h3>\n

\u062f\u0631 \u0631\u0648\u0634 FTCS \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0635\u0648\u0631\u062a \u062a\u0641\u0627\u0636\u0644 \u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646 \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646 \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f. \u0641\u0631\u0645 \u06a9\u0644\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u06af\u0633\u0633\u062a\u0647 \u0634\u062f\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0642\u0627\u0644\u0628 \u0645\u0639\u0627\u062f\u0644\u0647 (29) \u0628\u06cc\u0627\u0646 \u0634\u062f\u0647 \u0648 \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 [(t\u2206) \u0648 2<\/sup>(x\u2206) \u0648 2<\/sup>(y\u2206)]<\/em> \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0622\u0646\u0627\u0644\u06cc\u0632 \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u062f \u06a9\u0647 \u0631\u0648\u0634 \u0645\u0630\u06a9\u0648\u0631 \u062a\u062d\u062a \u0634\u0631\u0627\u0626\u0637 \u062d\u0627\u06a9\u0645 \u0628\u0631 \u0631\u0627\u0628\u0637\u0647 (30) \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u0631\u0648\u0634<\/p>\n

\u0646\u062a\u0627\u06cc\u062c \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0634\u06a9\u0644 (12) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

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

 <\/p>\n

\u0631\u0648\u0634 \u0636\u0645\u0646\u06cc <\/strong>ADI<\/strong><\/span><\/h3>\n

\u062f\u0631 \u0635\u0648\u0631\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0636\u0645\u0646\u06cc \u0628\u0631\u0627\u06cc \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0633\u0647\u0645\u0648\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0630\u06a9\u0648\u0631 \u0628\u0641\u0631\u0645 \u0631\u0627\u0628\u0637\u0647 (31) \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0622\u0646 \u0631\u0627 \u0647\u0645\u0627\u0646\u0646\u062f \u0645\u0639\u0627\u062f\u0644\u0647 (32) \u0645\u0631\u062a\u0628 \u0646\u0645\u0648\u062f. \u0628\u0627 \u0646\u06af\u0627\u0647\u06cc \u062f\u0642\u06cc\u0642\u062a\u0631 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (32) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631\u06cc\u0627\u0641\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0622\u0646 \u0628\u0647 \u06cc\u06a9 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a 5 \u0642\u0637\u0631\u06cc \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0647\u0645 \u0628\u0627\u0639\u062b \u0627\u0641\u0632\u0627\u06cc\u0634 \u062d\u062c\u0645 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0648 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 ADI (\u0645\u0628\u062d\u062b \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc<\/strong><\/span><\/a> \u0648 \u062d\u0644 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc<\/strong><\/span><\/a>) \u0631\u0648\u0646\u062f \u062d\u0644 \u0628\u0647 \u062f\u0648 \u0645\u0631\u062d\u0644\u0647 \u062a\u0642\u0633\u06cc\u0645 \u0634\u062f\u0647 \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u062f\u0648 \u0645\u0631\u062d\u0644\u0647\u060c \u062d\u0644 \u0628\u0627 \u062c\u0627\u0631\u0648\u0628 \u06a9\u0631\u062f\u0646 \u0645\u062c\u0647\u0648\u0644\u0627\u062a \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u0631 \u062c\u0647\u062a i \u0648 \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u0631 \u062c\u0647\u062a j\u00a0 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u062f\u0631 \u0647\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u062c\u0627\u06cc \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u067e\u0646\u062c \u0642\u0637\u0631\u06cc \u06cc\u06a9 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647 \u0642\u0637\u0631\u06cc \u062d\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc\u060c \u0641\u0631\u0645 \u06af\u0633\u0633\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (32) \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 ADI \u0628\u0635\u0648\u0631\u062a \u0631\u0648\u0627\u0628\u0637 (34) \u0648 (35) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. <\/span>\u0627\u06cc\u0646 \u0631\u0648\u0634 \u0627\u0632 \u0645\u0631\u062a\u0628\u0647 [(t\u2206) \u0648 2<\/sup>(x\u2206) \u0648 2<\/sup>(y\u2206)]<\/em> \u0628\u0648\u062f\u0647 \u0648 \u0628\u06cc \u0642\u06cc\u062f \u0648 \u0634\u0631\u0637 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a. \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0641\u0648\u0642 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0641\u0631\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0648 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a (36) \u0648 (37) \u0646\u0648\u0634\u062a.<\/span><\/p>\n

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

\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\u0644-2 \u062f\u0631 \u0634\u06a9\u0644 (13) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

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

\u0634\u06a9\u0644-13: \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0631\u0648\u06cc \u0633\u0637\u062d \u062f\u0631 \u0632\u0645\u0627\u0646\u0647\u0627\u06cc \u0627\u0644\u0641: 5 \u062b\u0627\u0646\u06cc\u0647\u060c \u0628: 30 \u062b\u0627\u0646\u06cc\u0647 \u0648 \u062c: 90 \u062b\u0627\u0646\u06cc\u0647 (\u0631\u0648\u0634 ADI).<\/span><\/strong><\/h5>\n

 <\/p>\n

 <\/p>\n

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

Stanley J. Farlow, “Partial Differential Equations for Scientists and engineers”, Dover Publications INC, New York, 1993<\/span><\/strong><\/p>\n

 <\/p>\n

\n
\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

\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc<\/strong><\/a><\/span><\/h4>\n

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc (\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0648\u062c \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0648 \u062f\u0648 \u0628\u0639\u062f\u06cc) \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/a><\/span><\/h4>\n

\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

\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\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<\/div>\n<\/div>\n

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

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f Solving Parabolic PDEs Using FDM \u0628\u0645\u0646\u0638\u0648\u0631 \u0628\u0631\u0631\u0633\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u06cc\u06a9 \u0648 \u062f\u0648 \u0628\u0639\u062f\u06cc \u06af\u0631\u0645\u0627 \u0645\u062f \u0646\u0638\u0631 \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062a\u0639\u062f\u062f\u06cc \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc… Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":11956,"parent":3477,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-11998","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\n\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\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=\"\u0631\u0648\u0634\u200c\u0647\u0627\u064a \u0645\u062a\u0639\u062f\u062f\u064a \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0628\u0631\u0627\u06cc \u0641\u0636\u0627\u0647\u0627\u06cc\u06cc \u064a\u0643 \u0628\u0639\u062f\u064a (\u0645\u0639\u0627\u062f\u0644\u0647 1\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 17) \u0648 \u062f\u0648 \u0628\u0639\u062f\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 28) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f ...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/solving-parabolic-pdes-using-fdm\/\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f - cfd-mrk\" \/>\n<meta property=\"og:description\" content=\"\u0631\u0648\u0634\u200c\u0647\u0627\u064a \u0645\u062a\u0639\u062f\u062f\u064a \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0628\u0631\u0627\u06cc \u0641\u0636\u0627\u0647\u0627\u06cc\u06cc \u064a\u0643 \u0628\u0639\u062f\u064a (\u0645\u0639\u0627\u062f\u0644\u0647 1\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 17) \u0648 \u062f\u0648 \u0628\u0639\u062f\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 28) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f ...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/solving-parabolic-pdes-using-fdm\/\" \/>\n<meta property=\"og:site_name\" content=\"cfd-mrk\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-28T05:41:20+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/11\/parabolic-equation-cover.png\" \/>\n\t<meta property=\"og:image:width\" content=\"825\" \/>\n\t<meta property=\"og:image:height\" content=\"345\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0632\u0645\u0627\u0646 \u062a\u0642\u0631\u06cc\u0628\u06cc \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646\" \/>\n\t<meta name=\"twitter:data1\" content=\"13 \u062f\u0642\u06cc\u0642\u0647\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/cfd-mrk.ir\\\/index.php\\\/training\\\/flow-analysis\\\/fundamentals-of-cfd\\\/solving-parabolic-pdes-using-fdm\\\/\",\"url\":\"https:\\\/\\\/cfd-mrk.ir\\\/index.php\\\/training\\\/flow-analysis\\\/fundamentals-of-cfd\\\/solving-parabolic-pdes-using-fdm\\\/\",\"name\":\"\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f - cfd-mrk\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/cfd-mrk.ir\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/cfd-mrk.ir\\\/index.php\\\/training\\\/flow-analysis\\\/fundamentals-of-cfd\\\/solving-parabolic-pdes-using-fdm\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/cfd-mrk.ir\\\/index.php\\\/training\\\/flow-analysis\\\/fundamentals-of-cfd\\\/solving-parabolic-pdes-using-fdm\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/cfd-mrk.ir\\\/wp-content\\\/uploads\\\/2021\\\/11\\\/parabolic-equation-cover.png\",\"datePublished\":\"2021-11-28T04:50:45+00:00\",\"dateModified\":\"2021-11-28T05:41:20+00:00\",\"description\":\"\u0631\u0648\u0634\u200c\u0647\u0627\u064a \u0645\u062a\u0639\u062f\u062f\u064a \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0628\u0631\u0627\u06cc \u0641\u0636\u0627\u0647\u0627\u06cc\u06cc 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