{"id":11653,"date":"2021-10-29T21:09:58","date_gmt":"2021-10-29T17:39:58","guid":{"rendered":"https:\/\/cfd-mrk.ir\/?page_id=11653"},"modified":"2021-11-28T09:26:07","modified_gmt":"2021-11-28T05:56:07","slug":"solving-elliptic-pdes-using-fdm","status":"publish","type":"page","link":"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/solving-elliptic-pdes-using-fdm\/","title":{"rendered":"\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\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 \u0628\u06cc\u0636\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/span><\/h2>\n

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

 <\/p>\n

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0645\u0648\u0636\u0648\u0639 \u0627\u06cc\u0646 \u067e\u0633\u062a \u0627\u0633\u062a. \u0635\u0628\u0642 \u0645\u0637\u0627\u0644\u0628 \u0645\u0646\u062f\u0631\u062c \u062f\u0631 \u062f\u0631 \u067e\u0633\u062a \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/span><\/a> \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0634\u06a9\u0644 (1)\u060c \u062a\u0627\u0628\u0639 u(x,y)<\/strong> \u0628\u0647 \u0641\u0631\u0645\u0647\u0627\u06cc \u0632\u06cc\u0631 \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f:<\/span><\/p>\n

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

\u0628\u0627 \u062a\u0631\u06a9\u06cc\u0628 \u0631\u0648\u0627\u0628\u0637 \u0641\u0648\u0642 \u062f\u0631 \u062d\u0627\u0644\u062a\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0639\u0645\u0644\u06af\u0631\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f. \u0645\u062a\u062f\u0627\u0648\u0644\u200c\u062a\u0631\u06cc\u0646 \u0631\u0648\u0634 \u0645\u0648\u062c\u0648\u062f \u0628\u0631\u0627\u06cc \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f\u060c \u0641\u0631\u0645\u0648\u0644 \u067e\u0646\u0686 \u0646\u0642\u0637\u0647 (Five Point Formula ) \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0646\u062e\u0633\u062a\u06cc\u0646 \u0628\u0627\u0631 \u062a\u0648\u0633\u0637 \u0631\u0627\u0646\u06af \u062f\u0631 \u0633\u0627\u0644 1908 \u0627\u0631\u0627\u0626\u0647 \u06af\u0631\u062f\u06cc\u062f [1]. \u062f\u0631 \u0641\u0631\u0645\u0648\u0644 \u067e\u0646\u062c \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u0639\u0644\u0627\u0648\u0647 \u0628\u0631 \u06af\u0631\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0645\u0648\u0631\u062f \u0628\u062d\u062b (\u06af\u0631\u0647 i, j)\u060c \u0686\u0647\u0627\u0631 \u06af\u0631\u0647 \u062f\u06cc\u06af\u0631 \u06a9\u0647 \u0647\u0645\u0633\u0627\u06cc\u0647\u200c\u0647\u0627\u06cc \u06af\u0631\u0647 \u0645\u0630\u06a9\u0648\u0631 \u0647\u0633\u062a\u0646\u062f\u060c \u0646\u06cc\u0632 \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0634\u0631\u06a9\u062a \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f (\u0634\u06a9\u06441).<\/span><\/p>\n

\u062f\u0631 \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u0627 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 (\u0645\u0639\u0627\u062f\u0644\u0647 1<\/strong><\/span><\/a>) \u0628\u0631\u0627\u0633\u0627\u0633 \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u0628\u0627 \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a. \u0641\u0631\u0645 \u06af\u0633\u0633\u062a\u0647\u200c\u0634\u062f\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0628\u0635\u0648\u0631\u062a (\u0645\u0639\u0627\u062f\u0644\u0647 13) \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0634\u0628\u06a9\u0647\u200c \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0627 \u0645\u0639\u0627\u062f\u0644\u0647 (13) \u0647\u0645\u0627\u0646\u0646\u062f \u0634\u06a9\u0644 (1) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

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

\u0634\u06a9\u0644-1: \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u06af\u06cc\u0631 \u0634\u0628\u06a9\u0647 \u062f\u0631 \u0631\u0648\u0634 \u0641\u0631\u0645\u0648\u0644 \u067e\u0646\u062c \u0646\u0642\u0637\u0647.<\/strong><\/span><\/h6>\n

\u00a0\u0644\u0627\u0632\u0645 \u0628\u0647 \u062a\u0648\u0636\u06cc\u062d \u0627\u0633\u062a \u06a9\u0647 \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0628\u0627 \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u0628\u0627\u0644\u0627\u062a\u0631 \u0646\u06cc\u0632 \u0627\u0645\u06a9\u0627\u0646 \u067e\u0630\u06cc\u0631 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0627\u0632 \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u062a\u0641\u0627\u0636\u0644 \u0645\u0631\u06a9\u0632\u06cc \u0628\u0627 \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u0686\u0647\u0627\u0631\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0628\u0647 \u0641\u0631\u0645\u0648\u0644 \u0646\u0647 (9) \u0646\u0642\u0637\u0647 \u0645\u0639\u0631\u0648\u0641 \u0627\u0633\u062a (\u0634\u06a9\u06442). \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0641\u0631\u0645 \u06af\u0633\u0633\u062a\u0647\u200c\u0634\u062f\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0628\u0627 \u062f\u0642\u062a \u0645\u0631\u062a\u0628\u0647 \u0686\u0647\u0627\u0631\u0645 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (14) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0634\u0628\u06a9\u0647 \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0627 \u0641\u0631\u0645\u0648\u0644 \u0646\u0647\u200c \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u0646\u06cc\u0632 \u0647\u0645\u0627\u0646\u0646\u062f \u0634\u06a9\u0644 (2) \u0627\u0633\u062a.<\/span><\/p>\n

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

\u0634\u06a9\u0644-2: \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u06af\u06cc\u0631 \u0634\u0628\u06a9\u0647 \u062f\u0631 \u0631\u0648\u0634 \u0641\u0631\u0645\u0648\u0644 \u0646\u0647 \u0646\u0642\u0637\u0647.<\/strong><\/span><\/h6>\n

\u0641\u0631\u0645\u0648\u0644 \u067e\u0646\u062c \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0635\u0648\u0631\u062a \u0627\u0633\u062a\u0646\u0633\u06cc\u0644 \u0628\u0639\u0644\u0627\u0648\u0647\u200c\u0627\u06cc (\u0634\u06a9\u06443) \u0628\u0627 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (13) \u06cc\u0627 \u0627\u0633\u062a\u0646\u0633\u06cc\u0644 \u0636\u0631\u0628\u062f\u0631\u06cc (\u0634\u06a9\u0644 4) \u0648 \u0628\u0627 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 (15) \u06cc\u0627 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0648 (\u0634\u06a9\u06445) \u0628\u0627 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 (16) \u0628\u06cc\u0627\u0646 \u0634\u0648\u062f. \u0647\u0631 \u0686\u0647 \u062a\u0639\u062f\u0627\u062f \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u062f\u0631\u06af\u06cc\u0631 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0634\u062f\u0647 \u0628\u06cc\u0634\u062a\u0631 \u0628\u0627\u0634\u062f\u060c \u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0622\u0646 \u0631\u0648\u0634 \u0628\u06cc\u0634\u062a\u0631 \u0627\u0633\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u0633\u062a\u0646\u0633\u06cc\u0644 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u067e\u0627\u06cc\u062f\u0627\u0631\u062a\u0631 \u0627\u0632 \u0627\u0633\u062a\u0646\u0633\u06cc\u0644\u200c\u0647\u0627\u06cc \u0628\u0639\u0644\u0627\u0648\u0647 \u0648 \u0636\u0631\u0628\u062f\u0631\u06cc \u0627\u0633\u062a. \u0627\u0644\u0628\u062a\u0647 \u0628\u0633\u062a\u0647 \u0628\u0647 \u0646\u0648\u0639 \u0645\u0633\u0626\u0644\u0647\u060c \u06a9\u0627\u0631\u0627\u06cc\u06cc \u0627\u06cc\u0646 \u0646\u0648\u0639 \u0627\u0633\u062a\u0646\u0633\u06cc\u0644\u200c\u0647\u0627 \u062a\u0641\u0627\u0648\u062a \u062f\u0627\u0631\u062f. \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u062f\u0631 \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0647\u062f\u0627\u06cc\u062a \u062f\u0631 \u06cc\u06a9 \u0635\u0641\u062d\u0647 \u0641\u0644\u0632\u06cc\u060c \u0628\u0645\u0646\u0638\u0648\u0631 \u062f\u062e\u0627\u0644\u062a \u062f\u0627\u062f\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0631\u0632\u0647\u0627 \u062f\u0631 \u06af\u0648\u0634\u0647\u200c\u0647\u0627 \u0628\u0647\u062a\u0631 \u0627\u0633\u062a \u0627\u0632 \u0627\u0633\u062a\u0646\u0633\u06cc\u0644\u200c\u0647\u0627\u06cc \u0636\u0631\u0628\u062f\u0631\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0646\u0645\u0648\u062f.<\/span><\/p>\n

\"\u0627\u0633\u062a\u0646\u0633\u06cc\u0644<\/p>\n

\u0634\u06a9\u0644-3: \u0627\u0633\u062a\u0646\u0633\u06cc\u0644 \u0628\u0639\u0644\u0627\u0648\u0647\u200c\u0627\u06cc.<\/span><\/strong><\/h6>\n
\"\u0627\u0633\u062a\u0646\u0633\u06cc\u0644<\/h6>\n
\u0634\u06a9\u0644-4: \u0627\u0633\u062a\u0646\u0633\u06cc\u0644 \u0636\u0631\u0628\u062f\u0631\u06cc.<\/span><\/strong><\/h6>\n
\"\u0627\u0633\u062a\u0646\u0633\u06cc\u0644<\/h6>\n
\u0634\u06a9\u0644-5: \u0627\u0633\u062a\u0646\u0633\u06cc\u0644 \u062a\u0631\u06a9\u06cc\u0628\u06cc.<\/span><\/strong><\/h6>\n

\u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0644 \u0633\u06cc\u0633\u062a\u0645 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062c\u0628\u0631\u06cc \u0628\u0647 \u062f\u0648 \u062f\u0633\u062a\u0647 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0648 \u062a\u06a9\u0631\u0627\u0631 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f (\u0627\u06cc\u0646\u062c\u0627<\/strong><\/span><\/a>). \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0644 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0634\u0627\u0645\u0644 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u06a9\u0631\u0627\u0645\u0631 \u0648 \u062d\u0630\u0641\u06cc \u06af\u0648\u0633 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f \u06a9\u0647 \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u0622\u0646\u0647\u0627 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627<\/strong><\/span><\/a>\u00a0\u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627 \u0645\u0639\u0645\u0648\u0644\u0627\u064b \u062f\u0627\u0631\u0627\u06cc \u0645\u062d\u062f\u0648\u062f\u06cc\u062a\u0647\u0627\u06cc\u06cc \u0646\u0638\u06cc\u0631 \u0645\u062d\u062f\u0648\u062f \u0628\u0648\u062f\u0646 \u0628\u0647 \u0633\u06cc\u0633\u062a\u0645 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u062e\u062a\u0635\u0627\u062a \u06a9\u0627\u0631\u062a\u0632\u06cc\u0646\u060c \u062f\u0627\u0645\u0646\u0647 \u0645\u06a9\u0639\u0628 \u0645\u0633\u062a\u0637\u06cc\u0644\u06cc\u060c \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc\u060c \u062d\u0627\u0641\u0638\u0647 \u0632\u06cc\u0627\u062f \u0631\u0627\u06cc\u0627\u0646\u0647 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0634\u06a9\u0644\u0627\u062a \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u0627\u0633\u062a. \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0644 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0648\u062f \u0646\u06cc\u0632 \u0628\u0647 \u062f\u0648 \u062f\u0633\u062a\u0647 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 (Point by Point ) (\u062a\u0646\u0647\u0627 \u062f\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u0645\u062c\u0647\u0648\u0644) \u0648 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637(Line by Line ) (\u0645\u0639\u0645\u0648\u0644\u0627\u064b \u062f\u0627\u0631\u0627\u06cc \u0633\u0647 \u0645\u062c\u0647\u0648\u0644) \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0644 \u062a\u06a9\u0631\u0627\u0631 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a\u0647\u0627\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0644 \u0645\u0633\u062a\u0642\u06cc\u0645 \u0631\u0627 \u0646\u062f\u0627\u0631\u062f. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0627\u0646\u0648\u0627\u0639 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0644 \u062a\u06a9\u0631\u0627\u0631 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u06a9\u0627\u0631\u0628\u0631\u062f \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0641\u0648\u0642 \u062f\u0631 \u0642\u0627\u0644\u0628 \u0645\u062b\u0627\u0644-1 \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

 <\/p>\n

\u0645\u062b\u0627\u0644-1:<\/strong><\/span><\/h3>\n

\u0628\u0639\u0646\u0648\u0627\u0646 \u0627\u0648\u0644\u06cc\u0646 \u0645\u062b\u0627\u0644\u060c \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u062d\u0627\u0644\u062a \u067e\u0627\u06cc\u0627 \u062f\u0631 \u062f\u0627\u062e\u0644 \u06cc\u06a9 \u0635\u0641\u062d\u0647 \u0686\u0647\u0627\u0631 \u0636\u0644\u0639\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a. \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 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f (\u0634\u06a9\u0644 6). \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc \u062f\u0645\u0627\u06cc\u06cc \u0646\u06cc\u0632 \u062f\u0631 \u0647\u0645\u06cc\u0646 \u0634\u06a9\u0644 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0627\u0632 \u0622\u0646\u062c\u0627\u0626\u06cc\u06a9\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0631\u0648\u06cc \u0645\u0631\u0632\u0647\u0627 \u0645\u0634\u062e\u0635 \u0627\u0633\u062a\u060c \u0634\u0631\u0637 \u0645\u0631\u0632\u06cc \u0627\u0632 \u0646\u0648\u0639 \u0634\u0631\u0637 \u0645\u0631\u0632\u06cc \u062f\u0631\u06cc\u0634\u0644\u0647 (Dirichlet) \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u062d\u0627\u06a9\u0645 \u0628\u0631 \u0627\u06cc\u0646 \u0645\u0633\u0626\u0644\u0647 (\u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u0647\u062f\u0627\u06cc\u062a \u062f\u0648 \u0628\u0639\u062f\u06cc)\u060c \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (17) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

\"\u0645\u0639\u0627\u062f\u0644\u0647<\/p>\n

\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 \u0627\u0632 \u0642\u0631\u0627\u0631 \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/span><\/p>\n

\"\u0634\u0631\u0627\u06cc\u0637<\/p>\n

\"\u0645\u0639\u0627\u062f\u0644\u0647<\/p>\n

\u0634\u06a9\u0644-6: \u0635\u0641\u062d\u0647 \u062a\u062e\u062a \u0686\u0647\u0627\u0631\u0636\u0644\u0639\u06cc \u0628\u0627 \u062a\u0648\u0632\u06cc\u0639 \u062b\u0627\u0628\u062a \u062f\u0645\u0627 \u062f\u0631 \u0645\u0631\u0632\u0647\u0627.<\/span><\/strong><\/h6>\n

\u067e\u0633 \u0627\u0632 \u0628\u0631\u0631\u0633\u06cc \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u062c\u0648\u0627\u0628\u200c\u0647\u0627 \u0627\u0632 \u0634\u0628\u06a9\u0647 (\u0647\u0645\u0627\u0646\u0646\u062f \u0634\u06a9\u0644-9)\u060c \u062f\u0631 \u062a\u0645\u0627\u0645\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc\u060c \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc 20 \u0627\u0644\u0645\u0627\u0646 \u062f\u0631 \u062c\u0647\u062a x \u0648 40 \u0627\u0644\u0645\u0627\u0646 \u062f\u0631 \u062c\u0647\u062a y \u062f\u0627\u0631\u062f (\u0634\u06a9\u0644-7).\u00a0<\/span><\/p>\n

\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/span><\/h3>\n

\u062f\u0631 \u0648\u0627\u0642\u0639 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0648 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0637 \u0628\u0647 \u062e\u0637 \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc \u062f\u0631 \u0645\u0633\u0627\u0626\u0644 \u0647\u0645\u0631\u0627\u0647 \u0628\u0627 \u062a\u0631\u0645 \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a. \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u062f\u0631 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0634\u0627\u0645\u0644 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u0698\u0627\u06a9\u0648\u0628\u06cc\u060c \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0648 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u200c\u0647\u0627 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.\u00a0<\/span><\/p>\n

 <\/p>\n

\u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u0698\u0627\u06a9\u0648\u0628\u06cc (Jacobi Point Iterative Method)<\/strong><\/span><\/h4>\n

\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634\u060c \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u062f\u0631 \u0647\u0631 \u06af\u0631\u0647 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0642\u0627\u062f\u06cc\u0631 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0647\u0645\u0633\u0627\u06cc\u0647 (\u0645\u0642\u0627\u062f\u06cc\u0631 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647 \u0627\u0632 \u062d\u062f\u0633 \u0627\u0648\u0644\u06cc\u0647 \u0648 \u06cc\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u062f\u0631 \u062a\u06a9\u0631\u0627\u0631 \u0642\u0628\u0644) \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 (18) \u0628\u06cc\u0627\u0646\u06af\u0631 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u0698\u0627\u06a9\u0648\u0628\u06cc \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u062f\u0627\u0631 uk+1<\/sup>i,j<\/sub><\/em><\/strong> \u062f\u0631 \u062a\u06a9\u0631\u0627\u0631 k+1<\/em><\/strong> \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0627\u0628\u0637\u0647 \u03b2=\u2206x\/\u2206y<\/em><\/strong> \u0648 k<\/em><\/strong> \u0645\u0631\u062d\u0644\u0647 \u062a\u06a9\u0631\u0627\u0631 \u0642\u0628\u0644\u06cc \u0627\u0633\u062a. \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u062a\u0627 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u062c\u0648\u0627\u0628\u200c\u0647\u0627 \u0628\u0647 \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u062f\u0644\u062e\u0648\u0627\u0647 \u0628\u0631\u0633\u062f \u0627\u062f\u0627\u0645\u0647 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u062f\u0644\u062e\u0648\u0627\u0647 \u0632\u0645\u0627\u0646\u06cc \u062a\u062d\u0642\u0642 \u067e\u06cc\u062f\u0627 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0628\u0627\u0642\u06cc\u0645\u0627\u0646\u062f\u0647 \u067e\u0627\u0633\u062e\u0647\u0627 \u0627\u0632 \u0645\u0642\u062f\u0627\u0631 \u0645\u0639\u06cc\u0646\u06cc \u06a9\u0645\u062a\u0631 \u0634\u0648\u062f (Err<\/strong><\/em>). \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 Err<\/strong><\/em> \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 (19) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u2005\u0634\u0648\u062f.<\/span><\/p>\n

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

\u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0641\u0648\u0642 Imax<\/sub><\/em><\/strong> \u0648 Jmax<\/sub><\/em><\/strong> \u062a\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u0627\u0646\u0647\u0627 \u062f\u0631 \u062c\u0647\u062a\u200c\u0647\u0627\u06cc x \u0648 y \u0627\u0633\u062a. \u0628\u0631\u0627\u06cc \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u062b\u0627\u0644-1 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u06a9\u0627\u0641\u06cc\u0633\u062a \u0628\u0627 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc T<\/em><\/strong> \u0628\u062c\u0627\u06cc u<\/em><\/strong> \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (18)\u060c \u0622\u0646 \u0631\u0627 \u062d\u0644 \u06a9\u0631\u062f. \u062c\u0648\u0627\u0628\u0647\u0627\u06cc \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u062f\u0631 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (8) \u0648 (9) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\"\u0634\u0628\u06a9\u0647<\/p>\n

\u0634\u06a9\u0644-7: \u0634\u0628\u06a9\u0647 \u0639\u062f\u062f \u062a\u0648\u0644\u06cc\u062f \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644-1.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u0634\u06a9\u0644-8: \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0628\u0627 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u0698\u0627\u06a9\u0648\u0628\u06cc.<\/span><\/strong><\/h6>\n

 <\/p>\n

\"\u0646\u062a\u0627\u06cc\u062c<\/span><\/p>\n

\u0634\u06a9\u0644-9: \u0686\u06af\u0648\u0646\u06af\u06cc \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u062f\u0631 \u0645\u0642\u0637\u0639 \u0645\u06cc\u0627\u0646\u06cc \u0633\u0637\u062d (\u062c\u0647\u062a y) \u0646\u0633\u062a \u0628\u0647 \u0627\u0628\u0639\u0627\u062f \u0634\u0628\u06a9\u0647.<\/span><\/strong><\/h6>\n

\u062f\u0631 \u0634\u06a9\u0644 (8) \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u06a9\u0647 \u0628\u0635\u0648\u0631\u062a \u0646\u06cc\u0645 \u0628\u06cc\u0636\u06cc \u0627\u0633\u062a. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0642\u0628\u0644\u0627\u064b \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u060c \u062f\u0631 \u0647\u0631 \u06a9\u0627\u0631 \u0639\u062f\u062f\u06cc\u060c \u062a\u0639\u062f\u0627\u062f \u0634\u0628\u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u06af\u0648\u0646\u0647\u200c\u0627\u06cc \u0628\u0627\u0634\u062f \u062a\u0627 \u062c\u0648\u0627\u0628\u200c\u0647\u0627\u06cc \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0645\u0633\u062a\u0642\u0644 \u0627\u0632 \u0634\u0628\u06a9\u0647 \u0628\u0627\u0634\u0646\u062f. \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631\u060c \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0628\u0631\u0627\u06cc \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0634\u06a9\u0644 (9) \u0631\u0633\u0645 \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 \u062a\u0641\u0627\u0648\u062a \u0686\u0646\u062f\u0627\u0646\u06cc \u062f\u0631 \u062c\u0648\u0627\u0628\u200c\u0647\u0627\u06cc \u0646\u0647\u0627\u06cc\u06cc \u0628\u06cc\u0646 \u0634\u0628\u06a9\u0647\u200c\u0647\u0627\u06cc 20*10 \u0648 30*15 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f. \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644 \u0628\u0631\u0627\u06cc \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u062a\u0645\u0627\u0645\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u0628\u06a9\u0627\u0631 \u0631\u0641\u062a\u0647 \u0645\u0633\u062a\u0642\u0644 \u0627\u0632 \u0634\u0628\u06a9\u0647 \u0628\u0627\u0634\u0646\u062f \u0627\u0632 \u0634\u0628\u06a9\u0647 40*20 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0622\u0646\u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

 <\/p>\n

\u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 (Gauss-Seidel Point Iterative Method)<\/strong><\/span><\/h4>\n

\u062f\u0631 \u0631\u0648\u0634 \u0645\u0630\u06a9\u0648\u0631 \u0647\u0631 \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u0628\u0647 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0628\u0644\u0627\u0641\u0627\u0635\u0644\u0647 \u067e\u0633 \u0627\u0632 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0646 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0628\u0639\u062f\u06cc \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u062c\u0632\u0626\u06cc\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627<\/strong><\/span><\/a> \u0622\u0645\u062f\u0647 \u0627\u0633\u062a. \u0628\u0627 \u0628\u06a9\u0627\u0631\u06af\u06cc\u0631\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0633\u0631\u0639\u062a \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u0628\u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u0645\u0644\u0627\u062d\u0638\u0647\u200c\u0627\u06cc \u062f\u0631 \u062d\u062f\u0648\u062f 100%\u00a0 \u0646\u0633\u0628\u062a \u0628\u0647 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u0698\u0627\u06a9\u0648\u0628\u06cc (\u062c\u062f\u0648\u0644 1) \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f (\u0634\u06a9\u0644\u200c\u0647\u0627\u06cc 20 \u0648 21).\u00a0 \u0641\u0631\u0645 \u06a9\u0644\u06cc \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0628\u0627 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0642\u0627\u0644\u0628 \u0631\u0648\u0634 \u0627\u062c\u0632\u0627\u0621 \u0645\u062d\u062f\u0648\u062f \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (20) \u0627\u0633\u062a. \u0646\u062a\u06cc\u062c\u0647 \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u062f\u0631 \u0634\u06a9\u0644 (10) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

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

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

\u0634\u06a9\u0644-10: \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0628\u0627 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644.<\/span><\/strong><\/h6>\n

 <\/p>\n

\u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc (Point Relaxation Iterative Method)<\/strong><\/span><\/h4>\n

\u062f\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631\u060c \u0641\u0631\u0622\u06cc\u0646\u062f \u062d\u0644 \u0627\u0632 \u06cc\u06a9 \u062d\u062f\u0633 \u0627\u0648\u0644\u06cc\u0647 \u0634\u0631\u0648\u0639 \u0634\u062f\u0647 \u0648 \u062a\u0627 \u062d\u0644 \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u062f\u0627\u0645\u0647 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. \u0686\u0646\u0627\u0646\u0686\u0647 \u062f\u0631 \u0637\u06cc \u0641\u0631\u0622\u06cc\u0646\u062f \u062d\u0644\u060c \u0631\u0648\u0646\u062f \u0648 \u0631\u0641\u062a\u0627\u0631 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0645\u062f \u0646\u0638\u0631 \u0628\u0627\u0634\u062f\u060c \u062c\u0647\u062a \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0627\u06cc \u0628\u0631\u0648\u0646\u06cc\u0627\u0628\u06cc \u0627\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u062f\u0631 \u062a\u06a9\u0631\u0627\u0631 \u0628\u0639\u062f\u06cc \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0642\u0631\u0627\u0631 \u06af\u06cc\u0631\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0646\u0631\u062e \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0627\u0641\u0632\u0627\u06cc\u0634 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u0698\u0627\u06a9\u0648\u0628\u06cc (\u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644-1 \u0628\u0637\u0648\u0631 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 15 \u0628\u0631\u0627\u0628\u0631) \u0648 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 (\u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644-1 \u0628\u0637\u0648\u0631 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 7.5 \u0628\u0631\u0627\u0628\u0631) \u0627\u0641\u0632\u0627\u06cc\u0634 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f. \u0627\u06cc\u0646 \u0645\u0647\u0645 \u062f\u0631 \u062c\u062f\u0648\u0644 (1) \u0648 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (20) \u0648 (21) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0645\u062a\u062f \u062d\u0627\u0636\u0631 \u0628\u0627 \u0639\u0646\u0648\u0627\u0646 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u06cc\u0627 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062e\u0644\u0627\u0635\u06cc \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0639\u0644\u0627\u0648\u0647 \u0628\u0631\u0627\u06cc\u0646 \u0628\u0631\u0627\u06cc \u0645\u0633\u0627\u0626\u0644\u06cc \u06a9\u0647 \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0622\u0646\u0647\u0627 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0627\u0645\u06a9\u0627\u0646\u200c\u067e\u0630\u06cc\u0631 \u0646\u0628\u0627\u0634\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u0645\u0646\u0627\u0633\u0628 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc\u060c \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0631\u0627 \u0628\u0647\u0628\u0648\u062f \u0628\u062e\u0634\u06cc\u062f.<\/span><\/p>\n

\u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u0646 \u0628\u0647 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0631\u0648\u0634 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc \u0627\u0628\u062a\u062f\u0627 \u0628\u0647 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633 \u0633\u0627\u06cc\u062f\u0644 (\u0645\u0639\u0627\u062f\u0644\u0647 20) \u06a9\u0647 \u0645\u0628\u0646\u0627\u06cc \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u062a\u0648\u062c\u0647 \u0634\u0648\u062f. \u0628\u0627 \u0627\u0641\u0632\u0648\u062f\u0646 \u062a\u0631\u0645 \u00a0uk<\/sup>i,j<\/sub> – uk<\/sup>i,j<\/sub><\/em><\/strong>\u0628\u0647 \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0630\u06a9\u0648\u0631 \u0648 \u062c\u0645\u0639 \u06a9\u0631\u062f\u0646 \u0622\u0646 \u0628\u0627 \u062a\u0631\u0645\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (21) \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0639\u0646\u0648\u0627\u0646 \u0641\u0631\u0622\u06cc\u0646\u062f \u062d\u0644\u060c uk<\/sup>i,j<\/sub><\/em><\/strong> \u0628\u0627\u06cc\u062f uk+1<\/sup>i,j<\/sub><\/em><\/strong> \u0631\u0627 \u062a\u0642\u0631\u06cc\u0628 \u0628\u0632\u0646\u062f. \u0628\u0647 \u0645\u0646\u0638\u0648\u0631 \u0634\u062a\u0627\u0628 \u062f\u0627\u062f\u0646 \u0628\u0647 \u0631\u0648\u0646\u062f \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u062d\u0644\u060c \u062a\u0631\u0645 \u062f\u0627\u062e\u0644 \u06a9\u0631\u0648\u0634\u0647 \u062f\u0631 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc\u060c \u03c9\u060c \u0636\u0631\u0628 \u0645\u06cc\u200c\u0634\u0648\u062f (\u0645\u0639\u0627\u062f\u0644\u064722). \u0628\u0627 \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647\u060c \u0641\u0631\u0645 \u0646\u0647\u0627\u06cc\u06cc \u06af\u0633\u0633\u062a\u0647\u200c\u0633\u0627\u0632\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0628\u0627 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (23) \u0646\u0648\u0634\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0631\u0627\u06cc \u03c9=1 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u03c9<1<\/strong><\/em> \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0627 \u0639\u0646\u0648\u0627\u0646 \u0631\u0648\u0634 \u0632\u06cc\u0631 \u062e\u0644\u0627\u0635\u06cc (Under Relaxation) \u0648 \u0628\u0631\u0627\u06cc \u03c9>1\u00a0 \u0628\u0627 \u0639\u0646\u0648\u0627\u0646 \u0631\u0648\u0634 \u0641\u0648\u0642 \u062e\u0644\u0627\u0635\u06cc (Over Relaxation) \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\n

<\/h5>\n

\u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0633\u0626\u0648\u0627\u0644\u06cc \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u0637\u0631\u062d \u0645\u06cc\u200c\u0628\u0627\u0634\u062f \u0627\u06cc\u0646\u0633\u062a \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647\u200c\u0627\u06cc \u0628\u0631\u0627\u06cc \u03c9 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u061f \u062f\u0631 \u067e\u0627\u0633\u062e \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u06af\u0641\u062a \u06a9\u0647 \u062f\u0631 \u0648\u0627\u0642\u0639 \u0647\u06cc\u0686 \u0631\u0627\u0647\u06a9\u0627\u0631 \u0645\u0634\u062e\u0635\u06cc \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647 \u03c9 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f. \u0627\u0645\u0627 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0645\u062d\u062f\u0648\u062f\u06cc\u060c \u0686\u0646\u062f\u06cc\u0646 \u0631\u0627\u0628\u0637\u0647 \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647 \u03c9 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0634\u062f\u0647 \u0627\u0633\u062a. \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0627\u0628\u0637 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u062f\u0631 \u062f\u0627\u0645\u0646\u0647 \u0645\u0631\u0628\u0639-\u0645\u0633\u062a\u0637\u06cc\u0644 \u0628\u0627 \u0634\u0631\u0637 \u0645\u0631\u0632\u06cc \u062f\u0631\u06cc\u0634\u0644\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (24) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

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

\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0647 (24) \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647 \u03c9 \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644-1 \u0628\u0631\u0627\u0628\u0631 1.995 \u062a\u0642\u0631\u06cc\u0628 \u0632\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc\u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647 \u0648\u0627\u0642\u0639\u06cc \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0628\u0631\u0627\u0628\u0631 1.85 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062f\u0631 \u0634\u06a9\u0644 (11) \u0646\u0645\u0648\u062f\u0627\u0631 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u06cc\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0628\u0631\u0627\u06cc \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc (1.85) \u062f\u0631 \u0634\u06a9\u0644 (12) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

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

\u0634\u06a9\u0644-11: \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc \u0648 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0628\u0627 \u0631\u0648\u0634 \u0646\u0642\u0637\u0647\u200c \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc.<\/span><\/strong><\/h6>\n

 <\/p>\n

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

\u0634\u06a9\u0644-12: \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0628\u0627 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc.<\/span><\/strong><\/h6>\n

 <\/p>\n

\u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062f\u0631 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/span><\/strong><\/h3>\n

\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0637 \u0628\u0647 \u062e\u0637 \u0645\u0639\u0627\u062f\u0644 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc \u062f\u0631 \u0645\u0633\u0627\u0626\u0644 \u0648\u0627\u0628\u0633\u062a\u0647 \u0628\u0647 \u0632\u0645\u0627\u0646 \u0627\u0633\u062a. \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062f\u0631 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644 \u0644\u0627\u067e\u0644\u0627\u0633 \u0634\u0627\u0645\u0644 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0637 \u0628\u0647 \u062e\u0637 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0648 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062e\u0644\u0627\u0635\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/span><\/p>\n

 <\/p>\n

\u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 (<\/strong>Gauss-Seidel Line Iterative Method<\/strong>)<\/strong><\/span><\/h4>\n

\u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u062f\u0631 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0631\u062f\u06cc\u0641\u200c\u0647\u0627\u06cc \u0633\u0637\u0631\u06cc \u06cc\u0627 \u0633\u062a\u0648\u0646\u06cc \u0634\u0628\u06a9\u0647 \u0647\u0645\u0632\u0645\u0627\u0646 \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0644\u062d\u0627\u0638 \u06af\u0634\u062a\u0647 \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0644\u0627\u0632\u0645\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0631\u062f\u06cc\u0641 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0644 \u0634\u0648\u062f. \u0628\u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631 \u062f\u0631 \u0647\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0633\u0647 \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u0645\u062c\u0647\u0648\u0644 \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u062f\u0631 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc (i-1, j)\u060c (i, j) \u0648 (i+1, j)<\/strong><\/em> \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f (\u0627\u06cc\u0646\u062c\u0627<\/strong><\/span><\/a>) \u06a9\u0647 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0622\u0646 \u0628\u0631\u0627\u06cc 2<i \u0648 i<Imax<\/sub>-1<\/strong><\/em>\u00a0 \u0637\u0628\u0642 \u0645\u0639\u0627\u062f\u0644\u0647 (26) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0630\u06a9\u0648\u0631 \u062f\u0631 \u0647\u0631 j \u062b\u0627\u0628\u062a\u060c \u0627\u0632 \u062a\u0645\u0627\u0645\u06cc \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0631\u062f\u06cc\u0641 i (\u06a9\u0647 \u0628\u0635\u0648\u0631\u062a \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u0631\u0628\u0639 \u0634\u06a9\u0644 \u062f\u0631 \u0634\u06a9\u0644 (13) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a) \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u062d\u0627\u0635\u0644 \u0627\u06cc\u0646 \u0627\u0645\u0631 \u062a\u0648\u0644\u06cc\u062f \u06cc\u06a9 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0636\u0631\u0627\u0626\u0628 \u0633\u0647 \u0642\u0637\u0631\u06cc \u0627\u0633\u062a. <\/span><\/p>\n

\u062f\u0631 \u0634\u06a9\u0644 (13) \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0644\u0648\u0632\u06cc \u0634\u06a9\u0644 \u0628\u06cc\u0627\u0646\u06af\u0631 \u0634\u0631\u0637 \u0645\u0631\u0632\u06cc\u060c \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0636\u0631\u0628\u062f\u0631 \u0645\u0639\u0631\u0641 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0639\u0644\u0648\u0645 \u062f\u0631 \u062a\u06a9\u0631\u0627\u0631 k+1\u060c \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0645\u0631\u0628\u0639 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0645\u062c\u0647\u0648\u0644\u0627\u062a \u062f\u0631 \u062a\u06a9\u0631\u0627\u0631 k+1 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u0648\u0646\u062f \u0648 \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u062f\u0627\u06cc\u0631\u0647 \u0634\u06a9\u0644 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0639\u0644\u0648\u0645 \u062f\u0631 \u062a\u06a9\u0631\u0627\u0631 k \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a \u06a9\u0647 \u0628\u0645\u0646\u0638\u0648\u0631 \u0627\u0639\u0645\u0627\u0644 \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (26) \u0628\u0631\u0627\u06cc \u0631\u062f\u06cc\u0641\u0647\u0627\u06cc i=1\u060c i=2 \u0648 i=Imax<\/sub>-1<\/strong> <\/em>\u0628\u0635\u0648\u0631\u062a \u0631\u0648\u0627\u0628\u0637 (27) \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

\"\u0686\u06cc\u062f\u0645\u0627\u0646<\/p>\n

\u0634\u06a9\u0644 13: \u0686\u06af\u0648\u0646\u06af\u06cc \u0642\u0631\u0627\u06af\u06cc\u0631\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062c\u0647\u0648\u0644 \u0648 \u0645\u0639\u0644\u0648\u0645 \u062f\u0631 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637\u06cc \u06af\u0648\u0633 \u0633\u0627\u06cc\u062f\u0644.<\/strong><\/span><\/h6>\n

\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0645\u0648\u062c\u0628 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0647\u0634\u062a\u0627\u062f \u062a\u0627 \u0646\u0648\u062f \u062f\u0631\u0635\u062f\u06cc \u0633\u0631\u0639\u062a \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0631\u0648\u0634 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0627\u0645\u0627 \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u0645\u0642\u062f\u0627\u0631 \u0632\u0645\u0627\u0646 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0645\u0631\u0627\u062a\u0628 \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0631\u0648\u0634 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0627\u0633\u062a. \u062f\u0631 \u0634\u06a9\u0644 (14) \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627\u06cc \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0627 \u0631\u0648\u0634 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc \u062f\u0631 \u0645\u0633\u0627\u0626\u0644\u06cc \u06a9\u0647 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u062f\u0631 \u06cc\u06a9 \u062c\u0647\u062a \u062e\u0627\u0635 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0628\u0627\u0634\u062f\u060c \u0628\u0647\u062a\u0631 \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644 \u062f\u0631 \u0622\u0646 \u062c\u0647\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/span><\/p>\n

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

\u0634\u06a9\u0644-14: \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0628\u0627 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u06af\u0648\u0633-\u0633\u0627\u06cc\u062f\u0644.<\/span><\/strong><\/h6>\n

 <\/p>\n

\u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062e\u0644\u0627\u0635\u06cc (Line<\/strong><\/span>\u00a0Relaxation Iterative Method<\/strong><\/span>)<\/strong><\/span><\/h4>\n

\u0647\u0645\u0627\u0646\u0646\u062f \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc\u060c \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062e\u0644\u0627\u0635\u06cc \u0646\u06cc\u0632 \u0627\u0632 \u06cc\u06a9 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u062c\u0628\u0631\u06cc \u062d\u0627\u06a9\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0628\u0627 \u0627\u0646\u062c\u0627\u0645 \u0631\u0627\u0647\u06a9\u0627\u0631 \u0645\u0634\u0627\u0628\u0647 \u062f\u0631 \u0642\u0633\u0645\u062a (\u0631\u0648\u0634 \u0646\u0642\u0637\u0647 \u0628\u0647 \u0646\u0642\u0637\u0647 \u062e\u0644\u0627\u0635\u06cc) \u0641\u0631\u0645 \u0646\u0647\u0627\u06cc\u06cc \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062e\u0644\u0627\u0635\u06cc \u0628\u0631\u0627\u06cc 2<i \u0648 i<Imax<\/sub>-1<\/strong><\/em> \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (28) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0628\u0647 \u0645\u0646\u0638\u0648\u0631 \u0627\u0639\u0645\u0627\u0644 \u0634\u0631\u0627\u0626\u0637 \u0645\u0631\u0632\u06cc \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (28) \u0628\u0631\u0627\u06cc \u0631\u062f\u06cc\u0641\u200c\u0647\u0627\u06cci=1\u060c i=2 \u0648 i=Imax<\/sub>-1<\/strong><\/em> \u0628\u0635\u0648\u0631\u062a \u0631\u0648\u0627\u0628\u0637 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u062f\u0633\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (29) \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

\u0647\u06cc\u0686\u06af\u0648\u0646\u0647 \u0631\u0648\u0634 \u0645\u0639\u06cc\u0646\u06cc \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647 \u03c9<\/strong> <\/em>\u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f. \u062f\u0631 \u0648\u0627\u0642\u0639 \u0627\u0632 \u0631\u0648\u0634 \u0633\u0639\u06cc \u0648 \u062e\u0637\u0627 \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u0645\u0646\u0627\u0633\u0628 \u03c9<\/strong> <\/em>\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u062f\u0631 \u0634\u06a9\u0644 (15) \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0646\u0633\u0628\u062a \u0628\u0647 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc \u0648 \u062f\u0631 \u0634\u06a9\u0644 (16) \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

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

\u0634\u06a9\u0644-15: \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc \u0648 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0628\u0627 \u0631\u0648\u0634 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062e\u0644\u0627\u0635\u06cc.<\/span><\/strong><\/h6>\n

 <\/p>\n

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

\u0634\u06a9\u0644-16: \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0628\u0627 \u0631\u0648\u0634 \u062a\u06a9\u0631\u0627\u0631 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u062e\u0644\u0627\u0635\u06cc.<\/span><\/strong><\/h6>\n

 <\/p>\n

\u0631\u0648\u0634\u200c<\/strong>(Alternative Direction Implicit (ADI))<\/strong><\/span><\/h4>\n

\u0631\u0648\u0634 ADI \u062f\u0631 \u0648\u0627\u0642\u0639 \u06cc\u06a9 \u0631\u0648\u0634 \u062e\u0637 \u0628\u0647 \u062e\u0637 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u0631 \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631 \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u0631 \u062c\u0647\u062a \u0633\u0637\u0631\u06cc \u0648 \u06cc\u06a9 \u0628\u0627\u0631 \u062f\u0631 \u062c\u0647\u062a \u0633\u062a\u0648\u0646\u06cc (\u0634\u06a9\u0644 17) \u0648 \u06cc\u0627 \u0628\u0631\u0639\u06a9\u0633 \u062d\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0641\u0631\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06a9\u0627\u0631 \u0631\u0641\u062a\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a (30) \u0648 (31) \u0627\u0633\u062a. \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (30) \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0628\u0637\u0648\u0631 \u0636\u0645\u0646\u06cc \u062f\u0631 \u062c\u0647\u062a i \u062d\u0644 \u0634\u062f\u0647 \u0648 \u0633\u067e\u0633 \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062a\u0635\u062d\u06cc\u062d \u0634\u062f\u0647 \u0628\u0637\u0648\u0631 \u0636\u0645\u0646\u06cc \u0648 \u062f\u0631 \u062c\u0647\u062a j \u062d\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0641\u0631\u0622\u06cc\u0646\u062f \u062d\u0644 \u0648 \u062f\u0631\u06af\u06cc\u0631 \u0634\u062f\u0646 \u06af\u0631\u0647\u200c\u0647\u0627 \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u062f\u0631 \u0634\u06a9\u0644 (17) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0631\u0648\u0646\u062f \u062d\u0644 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0627 \u062f\u062e\u0627\u0644\u062a \u062f\u0627\u062f\u0646 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc\u060c \u03c9<\/strong><\/em>\u060c \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (30) \u0648 (31) \u0633\u0631\u0639\u062a \u0628\u062e\u0634\u06cc\u062f. \u0641\u0631\u0645 \u062a\u0635\u062d\u06cc\u062d \u0634\u062f\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (32) \u0648 (33) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0647\u0645\u0627\u0646\u0646\u062f \u0633\u0627\u06cc\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u060c \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u062f\u0627\u0631 \u0628\u0647\u06cc\u0646\u0647 \u0628\u0631\u0627\u06cc \u03c9<\/strong><\/em> \u0628\u0633\u06cc\u0627\u0631 \u0645\u0634\u06a9\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u062a\u0646\u0647\u0627 \u0631\u0627\u0647 \u062d\u0644 \u0639\u0645\u0644\u06cc\u060c \u0628\u0631\u0631\u0633\u06cc \u062a\u062c\u0631\u0628\u06cc \u0647\u0645\u0631\u0627\u0647 \u0628\u0627 \u0633\u0639\u06cc \u0648 \u062e\u0637\u0627\u06cc \u0631\u0648\u0646\u062f \u062d\u0644 \u0628\u0627 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 \u03c9 <\/strong><\/em>\u0627\u0633\u062a.<\/span><\/p>\n

\"\u0686\u06af\u0648\u0646\u06af\u06cc<\/p>\n

\u0634\u06a9\u0644-17: \u0686\u06af\u0648\u0646\u06af\u06cc \u0686\u06cc\u062f\u0645\u0627\u0646 \u06af\u0631\u0647\u200c\u0647\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0628\u0631\u0627\u06cc \u0647\u0631 \u062a\u06a9\u0631\u0627\u0631.<\/span><\/strong><\/h6>\n

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

\u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0641\u0648\u0642 \u062a\u0646\u0647\u0627 \u0641\u0631\u0645 \u0633\u0627\u062f\u0647\u200c\u0627\u06cc \u0627\u0632 \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u0647 \u0631\u0648\u0634 ADI \u0627\u0633\u062a. \u0628\u0633\u062a\u0647 \u0628\u0647 \u0646\u0648\u0639 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0648 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0622\u0646 \u0641\u0631\u0645\u0648\u0644\u0627\u0633\u06cc\u0648\u0646 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u062a\u0641\u0627\u0648\u062a \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0633\u0631\u0639\u062a \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0646\u06cc\u0632 \u0628\u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0633\u0627\u06cc\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0637 \u0628\u0647 \u062e\u0637 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062e\u0644\u0627\u0635\u06cc \u0628\u06cc\u0634\u062a\u0631 \u0627\u0633\u062a. \u062f\u0631 \u0634\u06a9\u0644 (18) \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0633\u0631\u0639\u062a \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0634\u06a9\u0644 (19) \u0646\u06cc\u0632 \u0646\u0645\u0627\u06cc\u0634\u06af\u0631 \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627\u06cc \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\n

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

\u0634\u06a9\u0644-18: \u0636\u0631\u06cc\u0628 \u062e\u0644\u0627\u0635\u06cc \u0648 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u062a\u0646\u0627\u0638\u0631 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0628\u0627 \u0631\u0648\u0634 ADI.<\/span><\/strong><\/h6>\n

 <\/p>\n

\"\u062d\u0644<\/h6>\n
\u0634\u06a9\u0644-19: \u062a\u0648\u0632\u06cc\u0639 \u062f\u0645\u0627 \u0631\u0648\u06cc \u0633\u0637\u062d \u0628\u0627 \u0631\u0648\u0634 ADI.<\/span><\/strong><\/h6>\n

<\/h3>\n

\u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631<\/strong><\/span><\/h3>\n

\u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u062f\u0631 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0633\u0627\u0626\u0644 \u0628\u0627 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0628\u062d\u062b \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0648 \u0632\u0645\u0627\u0646 \u0647\u0645\u06af\u0631\u0627 \u0634\u062f\u0646 \u0645\u062d\u0627\u0633\u0628\u0627\u062a \u0645\u0637\u0631\u062d \u0627\u0633\u062a\u060c \u0644\u0630\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0642\u0633\u0645\u062a \u0633\u0639\u06cc \u0634\u062f\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0642\u0633\u0645\u062a\u200c\u0647\u0627\u06cc \u0642\u0628\u0644\u060c \u0627\u0632 \u0644\u062d\u0627\u0638 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0645\u0648\u0631\u062f \u0645\u0642\u0627\u06cc\u0633\u0647 \u0642\u0631\u0627\u0631 \u06af\u06cc\u0631\u0646\u062f. \u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a \u06a9\u0647 \u062f\u0631 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0645\u0633\u0627\u0626\u0644\u060c \u0628\u0639\u0644\u062a \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0627\u06a9\u0645 (\u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0628\u0648\u062f\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a)\u060c \u062d\u062c\u0645 \u0634\u0628\u06a9\u0647\u060c \u062d\u0627\u0641\u0638\u0647 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0648 \u062e\u06cc\u0644\u06cc \u0645\u0648\u0627\u0631\u062f \u062f\u06cc\u06af\u0631 \u0642\u0628\u0644 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u0637\u0631\u062d \u0628\u0627\u0634\u062f\u060c \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0622\u0646\u0647\u0627 \u0645\u0647\u0645 \u0627\u0633\u062a. \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062e\u0627\u0637\u0631 \u062a\u0623\u06a9\u06cc\u062f \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u0645\u0642\u0627\u06cc\u0633\u0647 \u062a\u0646\u0647\u0627 \u062f\u0631 \u0645\u0648\u0631\u062f \u0646\u0631\u062e \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u06cc\u06a9 \u0645\u0633\u0626\u0644\u0647 \u062e\u0627\u0635 \u0628\u0648\u062f\u0647 \u0648 \u0628\u0647\u062a\u0631\u06cc\u0646 \u0627\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627 \u0627\u0632 \u0644\u062d\u0627\u0638 \u0646\u0631\u062e \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0627\u0644\u0632\u0627\u0645\u0627\u064b \u0631\u0648\u0634 \u0628\u0647\u06cc\u0646\u0647 \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645\u06cc \u0645\u0633\u0627\u0626\u0644 \u0627\u06cc\u0646 \u062f\u0633\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/span><\/p>\n

\u0647\u0645\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0641\u0648\u0642 \u06a9\u0647 \u062f\u0631 \u0645\u062b\u0627\u0644-1 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0645\u0642\u062f\u0627\u0631 \u0628\u0627\u0642\u06cc\u0645\u0627\u0646\u062f\u0647 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0627\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627 \u06cc\u06a9\u0633\u0627\u0646 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0646\u062a\u0627\u06cc\u062c \u062d\u0627\u0635\u0644 \u0627\u0632 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0627\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627 \u062f\u0631 \u062c\u062f\u0648\u0644 (1)\u060c \u0634\u06a9\u0644 (20) \u0648 \u0646\u0645\u0648\u062f\u0627\u0631 \u0634\u06a9\u0644 (21) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\n

\u062c\u062f\u0648\u0644-1: \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u062f\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641.<\/strong><\/span><\/h6>\n

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

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

\u0634\u06a9\u0644-20: \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u062f\u0631 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641.<\/span><\/strong><\/h6>\n

 <\/p>\n

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

\u0634\u06a9\u0644-21: \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0628\u0631\u0627\u06cc \u0647\u0645\u06af\u0631\u0627\u0626\u06cc \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0628\u0627\u0642\u06cc\u0645\u0627\u0646\u062f\u0647 0.00001.<\/span><\/strong><\/h6>\n

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 <\/p>\n

\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

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

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\n

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

\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f Solving Elliptic PDEs Using FDM   \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0645\u0648\u0636\u0648\u0639 \u0627\u06cc\u0646 \u067e\u0633\u062a \u0627\u0633\u062a. \u0635\u0628\u0642 \u0645\u0637\u0627\u0644\u0628 \u0645\u0646\u062f\u0631\u062c \u062f\u0631 \u062f\u0631 \u067e\u0633\u062a \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0634\u06a9\u0644 (1)\u060c… Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":11680,"parent":3477,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-11653","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\n\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\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 \u0628\u06cc\u0636\u0648\u06cc \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0645\u0648\u0636\u0648\u0639 \u0627\u06cc\u0646 \u067e\u0633\u062a \u0627\u0633\u062a. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u067e\u0633\u062a \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f 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