{"id":10401,"date":"2020-12-05T14:27:19","date_gmt":"2020-12-05T10:57:19","guid":{"rendered":"https:\/\/cfd-mrk.ir\/?page_id=10401"},"modified":"2021-11-28T09:30:44","modified_gmt":"2021-11-28T06:00:44","slug":"partial-differential-equation","status":"publish","type":"page","link":"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/","title":{"rendered":"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc"},"content":{"rendered":"\r\n<h2 class=\"has-text-align-right has-black-color has-text-color wp-block-heading\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc<\/strong><\/h2>\r\n\r\n\r\n\r\n<h2 class=\"has-text-align-left has-black-color has-text-color wp-block-heading\"><strong>Partial Differential Equation<\/strong><\/h2>\r\n\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u06cc \u06af\u0641\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0622\u0646 \u062a\u0627\u0628\u0639 \u062f\u0648 \u06cc\u0627 \u0686\u0646\u062f \u0645\u062a\u063a\u06cc\u0631 \u0645\u0633\u062a\u0642\u0644 \u0628\u0648\u062f\u0647 \u06a9\u0647 \u0628\u0647 \u0634\u06a9\u0644 \u062a\u0631\u0645\u0647\u0627\u06cc \u0645\u0634\u062a\u0642\u06cc \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0638\u0627\u0647\u0631 \u0634\u062f\u0647 \u0628\u0627\u0634\u062f. \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0635\u0648\u0631\u062a\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0633\u062a\u0647\u200c\u0628\u0646\u062f\u06cc \u0646\u0645\u0648\u062f. \u062e\u0637\u06cc \u0628\u0648\u062f\u0646 \u06cc\u0627 \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0628\u0648\u062f\u0646\u060c \u062f\u0627\u0634\u062a\u0646 \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u06cc\u0627 \u062f\u0648\u0645\u060c \u0647\u0645\u0686\u0646\u06cc\u0646 \u0631\u0641\u062a\u0627\u0631 \u062d\u0644 \u0622\u0646\u0647\u0627 \u06a9\u0647 \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u0646\u0648\u0639 \u0641\u06cc\u0632\u06cc\u06a9 \u062d\u0627\u06a9\u0645 \u0627\u0633\u062a\u060c \u062f\u0633\u062a\u0647\u200c\u0628\u0646\u062f\u06cc\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0631\u0627 \u0645\u0639\u0631\u0641\u06cc \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f.<\/span><\/p>\r\n<h3 style=\"text-align: right;\"><strong><span style=\"color: #000000;\"><span style=\"color: #800000;\">\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc \u062e\u0637\u06cc \u0648 \u063a\u06cc\u0631 \u062e\u0637\u06cc<\/span><\/span><\/strong><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u062f\u0631 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062e\u0637\u06cc\u060c \u06a9\u0644\u06cc\u0647 \u062a\u0631\u0645\u0647\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u062e\u0637\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062f\u0631 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u067e\u0627\u0633\u062e\u0647\u0627\u06cc \u0645\u062c\u0632\u0627 \u0631\u0627 \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u062c\u0645\u0639 \u06a9\u0631\u062f\u0647 \u0648 \u067e\u0627\u0633\u062e \u062f\u06cc\u06af\u0631\u06cc \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u0635\u0644\u06cc \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f (\u0627\u0635\u0644 \u0628\u0631 \u0647\u0645 \u0646\u0647\u06cc \u06cc\u0627 \u0647\u0645\u0627\u0646 Superposition). \u0645\u0639\u0627\u062f\u0644\u0647 \u067e\u06cc\u0648\u0633\u062a\u06af\u06cc \u062c\u0631\u06cc\u0627\u0646\u0647\u0627\u06cc \u062a\u0631\u0627\u06a9\u0645\u200c\u067e\u0630\u06cc\u0631 (\u0645\u0639\u0627\u062f\u0644\u0647 1) \u0646\u0645\u0648\u0646\u0647\u200c\u0627\u06cc \u0627\u0632 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062e\u0637\u06cc \u0628\u0648\u062f\u0647 \u06a9\u0647 \u062f\u0631 \u0622\u0646<strong><em>\u200c<\/em><\/strong><strong><em>x<\/em><\/strong><strong><em>\u060c<\/em><\/strong> <strong><em>\u200c<\/em><\/strong><strong><em>y<\/em><\/strong> \u0648\u200c<strong><em>t <\/em><\/strong>\u00a0\u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u0648 \u200c\u200c\u200c\u200c\u200c\u200c\u200c<strong><em>\u03c1<\/em><\/strong>\u060c \u200c\u200c\u200c<strong><em>u<\/em><\/strong> \u00a0\u0648<strong><em>v <\/em><\/strong>\u00a0\u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 \u00a0\u00a0<\/span><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u06cc \u06af\u0641\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0648 \u06cc\u0627 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0622\u0646 (\u0648 \u06cc\u0627 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0648) \u062f\u0631 \u062a\u0631\u0645\u0647\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c\u0648\u062f \u0628\u0627\u0634\u062f. \u0628\u0631\u062e\u0644\u0627\u0641 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc\u060c \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u067e\u0627\u0633\u062e\u0647\u0627 \u0631\u0627 \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u062c\u0645\u0639 \u06a9\u0631\u062f\u0647 \u0648 \u067e\u0627\u0633\u062e \u062f\u06cc\u06af\u0631\u06cc \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u0635\u0644\u06cc \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 (2) \u0646\u0645\u0648\u0646\u0647\u200c\u0627\u06cc \u0627\u0632 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u0631 \u062d\u0642\u06cc\u0642\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u062d\u0631\u06a9\u062a \u062f\u0631 \u062c\u0647\u062a <strong><em>x<\/em><\/strong> \u062f\u0631 \u06cc\u06a9 \u062c\u0631\u06cc\u0627\u0646 \u062a\u0631\u0627\u06a9\u0645\u200c\u0646\u0627\u067e\u0630\u06cc\u0631 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (1) \u0648 (2) <strong><em>u<\/em><\/strong>\u060c <strong><em>v<\/em><\/strong>\u060c <strong><em>p<\/em><\/strong> \u0648<strong><em> \u03c1<\/em><\/strong> \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u0645\u0624\u0644\u0641\u0647 x \u0633\u0631\u0639\u062a\u060c \u0645\u0624\u0644\u0641\u0647 y \u0633\u0631\u0639\u062a\u060c \u0641\u0634\u0627\u0631 \u0627\u0633\u062a\u0627\u062a\u06cc\u06a9 \u0648 \u0686\u06af\u0627\u0644\u06cc \u0633\u06cc\u0627\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u0646\u062f. \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (2) <strong><em>\u03c5<\/em><\/strong> \u0636\u0631\u06cc\u0628 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0644\u0632\u062c\u062a \u0633\u06cc\u0646\u0645\u0627\u062a\u06cc\u06a9 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u062a\u0631\u0645\u0647\u0627\u06cc <strong><em>uu<sub>x<\/sub><\/em><\/strong> \u0648<strong><em>vu<sub>y<\/sub><\/em><\/strong> \u00a0(\u062c\u0645\u0644\u0627\u062a \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc: Convection Terms) \u062a\u0631\u0645\u0647\u0627\u06cc \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0645\u0634\u06a9\u0644\u200c\u0633\u0627\u0632\u062a\u0631\u06cc\u0646 \u062c\u0645\u0644\u0627\u062a \u0627\u0632 \u0644\u062d\u0627\u0638 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0646\u06cc\u0632 \u0645\u06cc\u200c\u0628\u0627\u0634\u0646\u062f. \u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a \u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644\u062a\u06cc \u062e\u0627\u0635 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0634\u0628\u0647 \u062e\u0637\u06cc (Quasi Linear) \u0646\u06cc\u0632 \u0645\u06cc\u200c\u06af\u0648\u06cc\u0646\u062f \u0648 \u0622\u0646 \u062d\u0627\u0644\u062a\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0646\u0633\u0628\u062a \u0628\u0647 \u0628\u0627\u0644\u0627\u062a\u0631\u06cc\u0646 \u0645\u0634\u062a\u0642 \u062e\u0648\u062f\u060c \u062e\u0637\u06cc \u0628\u0627\u0634\u062f.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10413 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-linear-and-nonliner.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u062e\u0637\u06cc \u0648 \u063a\u06cc\u0631 \u062e\u0637\u06cc\" width=\"1027\" height=\"157\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-linear-and-nonliner.png 1027w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-linear-and-nonliner-300x46.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-linear-and-nonliner-1024x157.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-linear-and-nonliner-768x117.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-linear-and-nonliner-360x55.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-linear-and-nonliner-600x92.png 600w\" sizes=\"auto, (max-width: 1027px) 100vw, 1027px\" \/><\/p>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #800000;\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0648 \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645<\/strong><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u062f\u0631\u062c\u0647 \u0645\u0634\u062a\u0642 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0646\u0633\u0628\u062a \u0628\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u0628\u06cc\u0627\u0646\u06af\u0631 \u0645\u0631\u062a\u0628\u0647 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 (3) \u0646\u0645\u0648\u0646\u0647\u200c\u0627\u06cc \u0627\u0632 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0648 \u0645\u0639\u0627\u062f\u0644\u0647 (4) \u0646\u0645\u0648\u0646\u0647\u200c\u0627\u06cc \u0627\u0632 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644\u06cc \u062c\u0632\u0626\u06cc \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u0627\u0633\u062a.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10417 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-First-and-Second-Order.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0645\u0631\u062a\u0628\u0647 \u0647\u0627\u06cc \u0627\u0648\u0644 \u0648 \u062f\u0648\u0645\" width=\"1038\" height=\"149\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-First-and-Second-Order.png 1038w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-First-and-Second-Order-300x43.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-First-and-Second-Order-1024x147.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-First-and-Second-Order-768x110.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-First-and-Second-Order-360x52.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-First-and-Second-Order-600x86.png 600w\" sizes=\"auto, (max-width: 1038px) 100vw, 1038px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639 \u0628\u0631\u0627\u06cc \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0646\u06cc\u0632 \u0635\u0627\u062f\u0642 \u0627\u0633\u062a. \u0628\u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 \u0645\u0631\u062a\u0628\u0647 \u0645\u0634\u062a\u0642 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u06cc\u06a9 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0627\u0646\u06af\u0631 \u0645\u0631\u062a\u0628\u0647 \u0622\u0646 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\">\u00a0<\/p>\r\n<h3 style=\"text-align: right;\"><strong><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc58012104\"><\/a><span style=\"color: #800000;\">\u062a\u0642\u0633\u06cc\u0645 \u0628\u0646\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc \u0627\u0632 \u0646\u0642\u0637\u0647 \u0646\u0638\u0631 \u0631\u0641\u062a\u0627\u0631 \u062d\u0644 \u0622\u0646\u0647\u0627<\/span><\/span><\/strong><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0648\u0634\u0647\u0627\u06cc \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u0646\u0648\u0639 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0627\u0632 \u0646\u0642\u0637\u0647 \u0646\u0638\u0631 \u0631\u0641\u062a\u0627\u0631 \u062d\u0644 \u0622\u0646\u0647\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0634\u062e\u0635\u0647\u200c\u0627\u06cc \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u0622\u0646\u0647\u0627\u0633\u062a. \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u0628\u0627 \u0622\u0648\u0631\u062f\u0646 \u0686\u0646\u062f \u0645\u062b\u0627\u0644 \u0627\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u0645\u0639\u0631\u0641\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0627\u06a9\u0645 \u0628\u0631 \u06cc\u06a9 \u062c\u0631\u06cc\u0627\u0646 \u062a\u0631\u0627\u06a9\u0645 \u067e\u0630\u06cc\u0631 \u063a\u06cc\u0631 \u0644\u0632\u062c \u0628\u0627 \u0641\u0631\u0636 \u063a\u06cc\u0631 \u0686\u0631\u062e\u0634\u06cc \u0628\u0648\u062f\u0646 \u0628\u0635\u0648\u0631\u062a \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (5) \u0645\u06cc \u0628\u0627\u0634\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 <strong><em>c<\/em><\/strong> \u0633\u0631\u0639\u062a \u0635\u0648\u062a \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062d\u0627\u0644 \u062c\u0647\u062a \u0627\u06cc\u062c\u0627\u062f \u062f\u0633\u062a\u06af\u0627\u0647\u06cc \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0634\u062e\u0635\u0647 \u0622\u0646 \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f\u060c \u0686\u0647\u0627\u0631 \u0645\u062c\u0647\u0648\u0644 <strong><em>u<sub>x<\/sub><\/em><\/strong>\u060c <strong><em>u<sub>y<\/sub><\/em><\/strong>\u060c <strong><em>v<sub>x<\/sub><\/em><\/strong> \u0648 <strong><em>v<sub>y<\/sub><\/em><\/strong> \u0631\u0627 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0630\u06a9\u0648\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a.<\/span><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\"> \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u0645\u062c\u0647\u0648\u0644\u0627\u062a \u0627\u0632 \u062a\u0639\u062f\u0627\u062f \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0645\u06cc \u0628\u0627\u0634\u062f\u060c \u0644\u0627\u0632\u0645\u0633\u062a \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u06a9\u0645\u06a9\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0646\u0645\u0648\u062f. \u0627\u0632 \u0622\u0646\u062c\u0627\u0626\u06cc\u06a9\u0647\u060c <em><strong>(<\/strong><\/em> <strong><em>u=f(x, y<\/em><\/strong> \u0648 <em><strong>(<\/strong><\/em> <strong><em>v=g(x, y<\/em><\/strong>\u00a0\u0645\u06cc \u0628\u0627\u0634\u062f\u060c \u0644\u0630\u0627 \u0628\u0627 \u0645\u0634\u062a\u0642 \u06af\u06cc\u0631\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u062f\u0648 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0642\u0627\u0646\u0648\u0646 \u0632\u0646\u062c\u06cc\u0631\u0647\u200c\u0627\u06cc (Chain Role) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u06a9\u0645\u06a9\u06cc (6) \u0631\u0627 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0646\u0645\u0648\u062f. \u0628\u0627 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (5) \u0648 (6) \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (7) \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u0634\u0648\u062f. \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (7) \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0635\u0648\u0631\u062a \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (8) \u0628\u0627\u0632 \u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u0628\u062f\u06cc\u0647\u06cc \u0627\u0633\u062a \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0648\u06cc\u0698\u0647 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (8)\u060c \u06a9\u0627\u0641\u06cc\u0633\u062a \u062f\u062a\u0631\u0645\u06cc\u0646\u0627\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0636\u0631\u0627\u0626\u0628 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0635\u0641\u0631 \u0645\u0646\u0638\u0648\u0631 \u06af\u0631\u062f\u062f. \u0644\u0630\u0627 \u0631\u0627\u0628\u0637\u0647 (9) \u0628\u0631\u0642\u0631\u0627\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0627\u0628\u0637\u0647 \u0641\u0648\u0642\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0631\u0631\u0633\u06cc \u0646\u0645\u0648\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u0645\u0634\u062e\u0635\u0647\u200c\u0627\u06cc \u0628\u0627 \u0634\u06cc\u0628 \u0645\u0634\u062e\u0635 (<strong><em>dy\/dx<\/em><\/strong>) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631. \u0644\u0630\u0627 \u0628\u0627 \u0645\u0639\u0627\u062f\u0644\u0647(10) \u0633\u0631\u0648\u06a9\u0627\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a.<\/span><\/p>\r\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10422 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-solution-behavior.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0648 \u0631\u0641\u062a\u0627\u0631 \u062d\u0644 \u0622\u0646\u200c\u0647\u0627\" width=\"1038\" height=\"733\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-solution-behavior.png 1038w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-solution-behavior-300x212.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-solution-behavior-1024x723.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-solution-behavior-768x542.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-solution-behavior-360x254.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-solution-behavior-600x424.png 600w\" sizes=\"auto, (max-width: 1038px) 100vw, 1038px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (10)\u060c <strong><em>M<\/em><\/strong> \u0639\u062f\u062f \u0645\u0627\u062e \u0628\u0648\u062f\u0647 \u06a9\u0647 \u0628\u0635\u0648\u0631\u062a <strong><em>V\/c<\/em><\/strong> \u062a\u0639\u0631\u06cc\u0641 \u0634\u062f\u0647 \u06a9\u0647 \u062f\u0631 \u0622\u0646 <strong><em>V<\/em><\/strong> \u0627\u0646\u062f\u0627\u0632\u0647 \u0633\u0631\u0639\u062a \u0648 <em><strong>c<\/strong><\/em> \u0633\u0631\u0639\u062a \u0635\u0648\u062a \u0645\u06cc\u200c\u0628\u0627\u0634\u0646\u062f. \u0628\u0627 \u0627\u0646\u062f\u06a9\u06cc \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u067e\u06cc \u0628\u0631\u062f \u06a9\u0647 \u0633\u0647 \u062d\u0627\u0644\u062a \u0628\u0631\u0627\u06cc \u0645\u0642\u062f\u0627\u0631 <strong><em>M<\/em><\/strong> \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/span><\/p>\r\n<h5 style=\"text-align: right;\"><span style=\"color: #ff6600;\"><strong> \u0627\u06cc\u0646 \u0633\u0647 \u062d\u0627\u0644\u062a \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/strong><\/span><\/h5>\r\n<ul style=\"text-align: right;\">\r\n<li><span style=\"color: #000000;\"><strong><em>1&gt;M<\/em><\/strong>\u061b \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0633\u0631\u0639\u062a \u062c\u0631\u06cc\u0627\u0646 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0633\u0631\u0639\u062a \u0635\u0648\u062a \u0645\u06cc\u200c\u0628\u0627\u0634\u062f \u0648 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0627\u0647\u06cc\u062a \u0628\u06cc\u0636\u0648\u06cc <span style=\"color: #ff0000;\"><strong>(Elliptic<\/strong><\/span>) \u062f\u0627\u0631\u062f. \u0628\u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631\u060c \u0647\u06cc\u0686\u06af\u0648\u0646\u0647 \u0645\u0642\u062f\u0627\u0631 \u0645\u0634\u062e\u0635\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f (\u062e\u0637 \u0645\u0634\u062e\u0635\u0647\u200c\u0627\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646 \u0634\u06cc\u0628 \u0622\u0646\u200c \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f).<\/span><\/li>\r\n<li><span style=\"color: #000000;\"><strong><em>1=M<\/em><\/strong> \u061b \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0633\u0631\u0639\u062a \u062c\u0631\u06cc\u0627\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0633\u0631\u0639\u062a \u0635\u0648\u062a \u0628\u0648\u062f\u0647 \u0648 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0627\u0647\u06cc\u062a \u0633\u0647\u0645\u0648\u06cc (<strong><span style=\"color: #ff0000;\">Parabolic<\/span><\/strong>) \u062f\u0627\u0631\u062f. \u0628\u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631\u060c \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0648\u06cc\u0698\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0628\u0631\u0627\u06cc \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0630\u06a9\u0648\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f (\u0641\u0642\u0637 \u06cc\u06a9 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u0628\u0627 \u0634\u06cc\u0628 \u0645\u0634\u062e\u0635 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f).<\/span><\/li>\r\n<li><span style=\"color: #000000;\"><strong><em>1&lt;M<\/em><\/strong> \u061b \u0633\u0631\u0639\u062a \u062c\u0631\u06cc\u0627\u0646 \u062f\u0631 \u0627\u06cc\u0646 \u062d\u0627\u0644\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0633\u0631\u0639\u062a \u0635\u0648\u062a \u0645\u06cc\u200c\u0628\u0627\u0634\u062f \u0648 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0627\u0647\u06cc\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc (<strong><span style=\"color: #ff0000;\">Hyperbolic<\/span><\/strong>) \u062f\u0627\u0631\u062f. \u0628\u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631\u060c \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u06cc\u0627\u062f \u0634\u062f\u0647 \u062f\u0627\u0631\u0627\u06cc \u062f\u0648 \u0645\u0642\u062f\u0627\u0631 \u0648\u06cc\u0698\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0627\u0633\u062a (\u062f\u0648 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u0628\u0627 \u0634\u06cc\u0628\u0647\u0627\u06cc \u0645\u0634\u062e\u0635 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f).<\/span><\/li>\r\n<\/ul>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u06a9\u0644\u06cc \u062f\u0631\u062c\u0647 \u062f\u0648\u0645 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 11) \u0648 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0642\u0627\u0646\u0648\u0646 \u0632\u0646\u062c\u06cc\u0631\u0647\u200c\u0627\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 (\u0645\u0639\u0627\u062f\u0644\u0647 12) \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u0646\u0645\u0648\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10425 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-chain-role.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc-\u0642\u0627\u0646\u0648\u0646 \u0632\u0646\u062c\u06cc\u0631\u0647\" width=\"1035\" height=\"490\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-chain-role.png 1035w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-chain-role-300x142.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-chain-role-1024x485.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-chain-role-768x364.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-chain-role-360x170.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-chain-role-600x284.png 600w\" sizes=\"auto, (max-width: 1035px) 100vw, 1035px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0647\u0645\u0627\u0646\u0646\u062f \u062d\u0627\u0644\u062a \u0642\u0628\u0644\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0627\u0647\u06cc\u062a \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (12) \u0631\u0627 \u0646\u06cc\u0632 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f. \u0628\u0627 \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (12) \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (13) \u0648 \u0628\u0627 \u0635\u0641\u0631 \u0645\u0646\u0638\u0648\u0631 \u0646\u0645\u0648\u062f\u0646 \u062f\u062a\u0631\u0645\u06cc\u0646\u0627\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0636\u0631\u0627\u0626\u0628 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647\u060c \u0631\u0627\u0628\u0637\u0647 (14) \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0627\u0628\u0637\u0647 (14) \u062d\u0627\u0644\u062a\u0647\u0627\u06cc \u0632\u06cc\u0631 \u0627\u0645\u06a9\u0627\u0646 \u067e\u0630\u06cc\u0631 \u0627\u0633\u062a:<\/span><\/p>\r\n<ul style=\"text-align: right;\">\r\n<li><span style=\"color: #000000;\"><strong><em>b<sup>2<\/sup>-4ac&lt;0<\/em><\/strong>\u061b \u0645\u0627\u0647\u06cc\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u06cc\u0636\u0648\u06cc \u0648 \u0647\u06cc\u0686 \u0645\u0642\u062f\u0627\u0631 \u0645\u0634\u062e\u0635\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f\u060c<\/span><\/li>\r\n<li><span style=\"color: #000000;\"><strong><em>\u0628\u0627 \u0634\u0631\u0637 b<sup>2<\/sup>-4ac=0<\/em><\/strong>\u061b \u0645\u0627\u0647\u06cc\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0633\u0647\u0645\u0648\u06cc \u0648 \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 \u0645\u0634\u062e\u0635\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0648<\/span><\/li>\r\n<li><span style=\"color: #000000;\"><strong><em>b<sup>2<\/sup>-4ac&gt;0<\/em><\/strong>\u061b \u0645\u0627\u0647\u06cc\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0648 \u062f\u0648 \u0645\u0642\u062f\u0627\u0631 \u0645\u0634\u062e\u0635\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/span><\/li>\r\n<\/ul>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc58012105\"><\/a><span style=\"color: #800000;\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc<\/strong><\/span><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0627\u06af\u0631 \u062f\u0631 \u0646\u0627\u062d\u06cc\u0647\u200c\u0627\u06cc\u060c \u062d\u0627\u0644\u062a 1 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10) \u0648 (14) \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u062f\u0631 \u0622\u0646 \u0646\u0627\u062d\u06cc\u0647 \u0645\u0627\u0647\u06cc\u062a \u0628\u06cc\u0636\u0648\u06cc \u062f\u0627\u0631\u062f. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0631\u0648\u0627\u0628\u0637 \u0645\u0634\u062e\u0635 \u0627\u0633\u062a\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0627\u062d\u06cc\u060c \u0627\u0632 \u0645\u0646\u062d\u0646\u06cc \u0645\u0634\u062e\u0635\u0647 \u0648\u0627\u0642\u0639\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0646\u06cc\u0633\u062a. \u0644\u0627\u0632\u0645 \u0628\u0647 \u0630\u06a9\u0631 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u06cc\u0636\u0648\u06cc \u0628\u0627 \u0639\u0646\u0648\u0627\u0646\u0647\u0627\u06cc \u0645\u0633\u0626\u0644\u0647 \u062a\u0639\u0627\u062f\u0644\u06cc(Equilibrium Problem) \u06cc\u0627 \u0645\u0633\u0626\u0644\u0647 \u062a\u0648\u0632\u06cc\u0639(Distribution Problem) \u0646\u06cc\u0632 \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f\u060c \u0686\u0631\u0627\u06a9\u0647 \u0627\u063a\u062a\u0634\u0627\u0634 \u0627\u06cc\u062c\u0627\u062f \u0634\u062f\u0647 \u062f\u0631 \u0647\u0631 \u0646\u0642\u0637\u0647 \u0628\u0637\u0648\u0631 \u06cc\u06a9\u0633\u0627\u0646 \u062f\u0631 \u0647\u0645\u0647 \u062c\u0647\u0627\u062a \u0645\u0646\u062a\u0634\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631 \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u06af\u0641\u062a \u06a9\u0647 \u062f\u0631 \u06cc\u06a9 \u062c\u0647\u062a \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0634\u062a\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0628\u0644\u06a9\u0647 \u0645\u06cc\u0632\u0627\u0646 \u062a\u0623\u062b\u06cc\u0631\u200c\u067e\u0630\u06cc\u0631\u06cc \u0648 \u062a\u0623\u062b\u06cc\u0631 \u06af\u0630\u0627\u0631\u06cc \u062f\u0631 \u062a\u0645\u0627\u0645 \u062c\u0647\u0627\u062a \u06cc\u06a9\u0633\u0627\u0646 \u0627\u0633\u062a (\u0634\u06a9\u0644 1). \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u062c\u0631\u06cc\u0627\u0646 \u062a\u0631\u0627\u06a9\u0645 \u0646\u0627\u067e\u0630\u06cc\u0631 \u062f\u0631 \u06cc\u06a9 \u062d\u0641\u0631\u0647 \u0627\u0634\u0627\u0631\u0647 \u06a9\u0631\u062f (\u0634\u06a9\u0644 2).<\/span><\/p>\r\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10430 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic.png\" alt=\"\u062a\u0648\u0632\u06cc\u0639 \u0627\u063a\u062a\u0634\u0627\u0634\u0627\u062a \u062f\u0631 \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\" width=\"998\" height=\"406\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic.png 998w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-300x122.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-768x312.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-360x146.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-600x244.png 600w\" sizes=\"auto, (max-width: 998px) 100vw, 998px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0627\u06cc\u062f \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a \u06a9\u0647 \u062f\u0631 \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 \u062f\u0631 \u0647\u06cc\u0686 \u06cc\u06a9 \u0627\u0632 \u0646\u0642\u0627\u0637 \u062f\u0627\u062e\u0644 \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc\u060c \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0647 \u0646\u0627\u0645\u0639\u06cc\u0646 \u0646\u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0627\u0632 \u0637\u0631\u0641\u06cc \u0647\u06cc\u0686\u06af\u0648\u0646\u0647 \u062c\u0647\u062a \u0645\u0634\u062e\u0635\u06cc(Characteristic Direction) \u0646\u06cc\u0632 \u062f\u0631 \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f. \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u067e\u0648\u0627\u0633\u0648\u0646 (15) \u0648 \u0644\u0627\u067e\u0644\u0627\u0633 (16) \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627\u06cc\u06cc \u0633\u0627\u062f\u0647 \u0627\u0632 \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 \u0647\u0633\u062a\u0646\u062f.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10432 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptical-equations.png\" alt=\"\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\" width=\"1028\" height=\"126\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptical-equations.png 1028w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptical-equations-300x37.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptical-equations-1024x126.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptical-equations-768x94.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptical-equations-360x44.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptical-equations-600x74.png 600w\" sizes=\"auto, (max-width: 1028px) 100vw, 1028px\" \/><\/p>\r\n<p><strong style=\"color: #000000; font-size: inherit; text-align: right;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10434 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-cavity.png\" alt=\"\u0634\u0645\u0627\u062a\u06cc\u06a9\u06cc \u0627\u0632 \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc\" width=\"896\" height=\"453\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-cavity.png 896w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-cavity-300x152.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-cavity-768x388.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-cavity-360x182.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Elliptic-cavity-600x303.png 600w\" sizes=\"auto, (max-width: 896px) 100vw, 896px\" \/> <\/strong><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc\u060c \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc \u0639\u0628\u0627\u0631\u062a\u0633\u062a \u0627\u0632:<\/span><\/p>\r\n<ul style=\"text-align: right;\">\r\n<li><span style=\"color: #000000;\">\u062f\u0627\u0645\u0646\u0647 \u062d\u0644 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0628\u06cc\u0636\u0648\u06cc \u0646\u0627\u062d\u06cc\u0647 \u0628\u0633\u062a\u0647\u200c\u0627\u06cc \u0627\u0633\u062a\u060c<\/span><\/li>\r\n<li><span style=\"color: #000000;\">\u0627\u063a\u062a\u0634\u0627\u0634\u0627\u062a \u062f\u0631 \u062a\u0645\u0627\u0645 \u062c\u0647\u0627\u062a \u0628\u0637\u0648\u0631 \u06cc\u06a9\u0633\u0627\u0646 \u0645\u0646\u062a\u0634\u0631 \u0645\u06cc\u200c\u06af\u0631\u062f\u062f \u0648<\/span><\/li>\r\n<li><span style=\"color: #000000;\">\u062d\u0644 \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 \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0646\u062f\u0627\u0631\u062f.<\/span><\/li>\r\n<\/ul>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc58012106\"><\/a><span style=\"color: #800000;\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc<\/strong><\/span><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0627\u06af\u0631 \u062f\u0631 \u062a\u0645\u0627\u0645 \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc\u060c \u062d\u0627\u0644\u062a \u0633\u0648\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10) \u0648 (14) \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc\u060c \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u062f\u0631 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u062f\u0627\u0642\u0644 \u062f\u0648 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0631\u0627 \u0628\u0647 \u0642\u0644\u0645\u0631\u0648\u0647\u0627\u06cc \u0633\u06a9\u0648\u062a\u060c \u062a\u0623\u062b\u06cc\u0631\u06af\u0630\u0627\u0631 \u0648 \u0645\u062a\u0623\u062b\u0631 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f. \u0631\u0698\u06cc\u0645\u0647\u0627\u06cc \u062c\u0631\u06cc\u0627\u0646 \u0645\u0627\u0641\u0648\u0642 \u0635\u0648\u062a \u0647\u0645\u0648\u0627\u0631\u0647 \u06cc\u06a9 \u0645\u0633\u0626\u0644\u0647 \u0645\u0642\u062f\u0627\u0631 \u0648\u06cc\u0698\u0647 \u0628\u0648\u062f\u0647 \u0648 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0627\u06a9\u0645 \u0628\u0631 \u0622\u0646\u0647\u0627 \u0627\u0632 \u0645\u0627\u0647\u06cc\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0627\u0633\u062a. \u062f\u0631 \u0634\u06a9\u0644 (3) \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0637\u0647 \u062f\u0631 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u062f\u0644\u062e\u0648\u0627\u0647 \u0627\u0632 \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0627\u063a\u0631\u0627\u0642 \u0622\u0645\u06cc\u0632 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a (\u0645\u0639\u0645\u0648\u0644\u0627\u064b \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u0627\u0646\u062d\u0646\u0627\u0621 \u062f\u0627\u0631\u062f). \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u062a\u062d\u062a \u0639\u0646\u0648\u0627\u0646 \u0645\u0633\u0627\u0626\u0644 \u0645\u0642\u062f\u0627\u0631 \u0648\u06cc\u0698\u0647(Eigen Value Problem) \u0646\u06cc\u0632 \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10438 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic.png\" alt=\"\u0646\u0648\u0627\u062d\u06cc \u0633\u06a9\u0648\u062a\u060c \u062a\u0623\u062b\u06cc\u0631\u06af\u0630\u0627\u0631 \u0648 \u0645\u062a\u0627\u062b\u0631 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0647\u0630\u0644\u0648\u0644\u0648\u06cc\" width=\"941\" height=\"458\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic.png 941w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-300x146.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-768x374.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-360x175.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-600x292.png 600w\" sizes=\"auto, (max-width: 941px) 100vw, 941px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0648\u062c\u0648\u062f \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u062f\u0631 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u063a\u062a\u0634\u0627\u0634\u0627\u062a \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u0627\u06cc\u0646 \u062e\u0637\u0648\u0637 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u06af\u06cc\u0631\u062f. \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 (17) \u0648 \u062f\u0648\u0645 (18) \u0645\u062b\u0627\u0644\u0647\u0627\u06cc \u0633\u0627\u062f\u0647\u200c\u0627\u06cc \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0648 \u062f\u0648\u0645 \u0627\u0633\u062a.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10440 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-Equations.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc\" width=\"1036\" height=\"125\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-Equations.png 1036w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-Equations-300x36.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-Equations-1024x124.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-Equations-768x93.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-Equations-360x43.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Hyperbolic-Equations-600x72.png 600w\" sizes=\"auto, (max-width: 1036px) 100vw, 1036px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u06a9\u0647 \u062f\u0631 \u0622\u0646\u0647\u0627 <em><strong>\u03b1<\/strong><\/em>\u00a0\u0633\u0631\u0639\u062a \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0633\u062a. \u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc\u060c \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0639\u0628\u0627\u0631\u062a\u0633\u062a \u0627\u0632:<\/span><\/p>\r\n<ul style=\"text-align: right;\">\r\n<li><span style=\"color: #000000;\">\u0627\u063a\u062a\u0634\u0627\u0634\u0627\u062a \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u0645\u0646\u062a\u0634\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li>\r\n<li><span style=\"color: #000000;\">\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc\u060c \u062f\u0627\u0631\u0627\u06cc \u062d\u062f\u0627\u0642\u0644 \u062f\u0648 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/li>\r\n<\/ul>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc58012107\"><\/a><span style=\"color: #800000;\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc<\/strong><\/span><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u062f\u0631 \u0635\u0648\u0631\u062a\u06cc\u06a9\u0647 \u062d\u0627\u0644\u062a \u062f\u0648\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10) \u0648 (14) \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0628\u0631\u0642\u0631\u0627\u0631 \u0628\u0627\u0634\u062f\u060c \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc\u060c \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0633\u0647\u0645\u0648\u06cc \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u062f\u0631 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0641\u0642\u0637 \u06cc\u06a9 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062f\u0627\u0645\u0646\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0631\u0627 \u0628\u0647 \u062f\u0648 \u0642\u0644\u0645\u0631\u0648 \u062a\u0623\u062b\u06cc\u0631\u06af\u0630\u0627\u0631 \u0648 \u0645\u062a\u0623\u062b\u0631 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f (\u0634\u06a9\u0644 4). \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u062a\u062d\u062a \u0639\u0646\u0648\u0627\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0646\u062a\u0634\u0627\u0631(Propagation Problem)\u00a0 \u0646\u06cc\u0632 \u0628\u06cc\u0627\u0646 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10443 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic.png\" alt=\"\u0646\u0648\u0627\u062d\u06cc \u062a\u0623\u062b\u06cc\u0631\u06af\u0630\u0627\u0631 \u0648 \u0645\u062a\u0623\u062b\u0631 \u062f\u0631 \u0633\u06cc\u0633\u062a\u0645\u0647\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u0633\u0647\u0645\u0648\u06cc\" width=\"841\" height=\"433\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic.png 841w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-300x154.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-768x395.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-360x185.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-600x309.png 600w\" sizes=\"auto, (max-width: 841px) 100vw, 841px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0641\u0631\u0622\u06cc\u0646\u062f \u062d\u0644 \u0639\u062f\u062f\u06cc \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0633\u0647\u0645\u0648\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0627\u0628\u062a\u062f\u0627\u06cc \u062c\u0631\u06cc\u0627\u0646 (\u0627\u0632 \u0646\u0638\u0631 \u0632\u0645\u0627\u0646\u06cc \u06cc\u0627 \u0645\u06a9\u0627\u0646\u06cc) \u0634\u0631\u0648\u0639 \u0648 \u0628\u0647 \u067e\u0627\u06cc\u06cc\u0646 \u062f\u0633\u062a \u062c\u0631\u06cc\u0627\u0646 \u067e\u06cc\u0634 \u0645\u06cc\u200c\u0631\u0648\u06cc\u0645(Marching). \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0648\u062c\u0648\u062f \u06cc\u06a9 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u062f\u0631 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u063a\u062a\u0634\u0627\u0634\u0627\u062a \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u0627\u06cc\u0646 \u062e\u0637 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062a\u0648\u062c\u0647 \u0634\u0648\u062f \u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u062d\u0627\u0644\u062a \u062e\u0627\u0635\u06cc \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u0646\u062a\u0642\u0627\u0644 \u062d\u0631\u0627\u0631\u062a \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0646\u0627\u067e\u0627\u06cc\u0627 (19) \u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u0646\u062a\u0634\u0627\u0631 \u0644\u0632\u062c\u062a (20) \u0646\u0645\u0648\u0646\u0647\u200c\u0647\u0627\u06cc\u06cc \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc \u0627\u0633\u062a.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10445 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-equations.png\" alt=\"\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\" width=\"1040\" height=\"142\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-equations.png 1040w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-equations-300x41.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-equations-1024x140.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-equations-768x105.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-equations-360x49.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/PDEs-Parabolic-equations-600x82.png 600w\" sizes=\"auto, (max-width: 1040px) 100vw, 1040px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0637\u0648\u0631 \u06a9\u0644\u06cc\u060c \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc \u0639\u0628\u0627\u0631\u062a\u0633\u062a \u0627\u0632:<\/span><\/p>\r\n<ul style=\"text-align: right;\">\r\n<li><span style=\"color: #000000;\">\u0627\u063a\u062a\u0634\u0627\u0634\u0627\u062a \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u062a\u0646\u0647\u0627 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u0645\u0648\u062c\u0648\u062f \u0645\u0646\u062a\u0634\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/li>\r\n<li><span style=\"color: #000000;\">\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\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u062e\u0637 \u0645\u0634\u062e\u0635\u0647 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/li>\r\n<\/ul>\r\n<p style=\"text-align: right;\">\u00a0<\/p>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc58012108\"><\/a><span style=\"color: #800000;\"><strong>\u0645\u0627\u0647\u06cc\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631- \u0627\u0633\u062a\u0648\u06a9\u0633<\/strong><\/span><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0627\u0633\u062a\u060c \u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u062f\u0631 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u06cc\u062f\u0627\u0646 \u062c\u0631\u06cc\u0627\u0646\u060c \u0639\u0645\u062f\u062a\u0627\u064b \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc \u06af\u06cc\u0631\u062f\u060c \u0644\u0630\u0627 \u0631\u0641\u062a\u0627\u0631\u0634\u0646\u0627\u0633\u06cc \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0632 \u0627\u0647\u0645\u06cc\u062a \u0648\u06cc\u0698\u0647\u200c\u0627\u06cc \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0627\u0633\u062a. \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0647\u0645\u0648\u06cc (\u062a\u0631\u0645 \u0632\u0645\u0627\u0646\u06cc)\u060c \u0647\u0630\u0644\u0648\u0644\u0648\u06cc (\u062a\u0631\u0645 \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc) \u0648 \u0628\u06cc\u0636\u0648\u06cc (\u062a\u0631\u0645\u0647\u0627\u06cc \u0644\u0632\u062c\u062a) \u0645\u06cc \u0628\u0627\u0634\u062f. \u0627\u0644\u0628\u062a\u0647 \u0628\u0633\u062a\u0647 \u0628\u0647 \u0646\u0648\u0639 \u062c\u0631\u06cc\u0627\u0646 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u0627\u0644\u0628 \u0628\u0627\u0634\u062f. \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u062f\u0631 \u062c\u0631\u06cc\u0627\u0646\u0647\u0627\u06cc \u0645\u0627\u0641\u0648\u0642 \u0635\u0648\u062a \u062a\u0631\u0645 \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc \u0627\u0632 \u0627\u0647\u0645\u06cc\u062a \u0628\u0633\u06cc\u0627\u0631 \u0628\u06cc\u0634\u062a\u0631\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u062a\u0631\u0645 \u0644\u0632\u062c\u062a \u0628\u0631\u062e\u0648\u0631\u062f\u0627\u0631 \u0628\u0648\u062f\u0647 \u0648 \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u0645\u0627\u0647\u06cc\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u062f\u0627\u0631\u062f. \u0628\u0631\u0639\u06a9\u0633\u060c \u062f\u0631 \u062c\u0631\u06cc\u0627\u0646\u0647\u0627\u06cc \u062f\u0627\u0631\u0627\u06cc \u0633\u0631\u0639\u062a \u06a9\u0645\u060c \u062a\u0631\u0645 \u0644\u0632\u062c\u062a \u063a\u0627\u0644\u0628 \u0628\u0648\u062f\u0647 \u0648 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u0631\u0641\u062a\u0627\u0631 \u0628\u06cc\u0636\u0648\u06cc \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u0634\u062a. \u062c\u0647\u062a \u062a\u0641\u06a9\u06cc\u06a9 \u0627\u06cc\u0646 \u0645\u0627\u0647\u06cc\u062a\u200c\u0647\u0627 \u0648 \u0628\u0631\u0631\u0633\u06cc \u0627\u0648\u0644\u06cc\u0647 \u0628\u0631\u062e\u0648\u0631\u062f\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u0628\u0627 \u062a\u0631\u0645\u200c\u0647\u0627\u06cc \u0645\u0634\u0627\u0628\u0647 \u062a\u0631\u0645\u0647\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u0633\u0639\u06cc \u0634\u062f\u0647 \u06a9\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644\u060c \u0644\u0627\u067e\u0644\u0627\u0633 \u0648 \u0627\u0646\u062a\u0634\u0627\u0631 (\u06af\u0631\u0645\u0627) \u06a9\u0647 \u0631\u062f \u067e\u0627\u0647\u0627\u06cc\u0634\u0627\u0646 \u0628\u0647 \u0646\u062d\u0648\u06cc \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0628\u0637\u0648\u0631 \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0645\u0648\u0631\u062f \u0628\u062d\u062b \u0642\u0631\u0627\u0631 \u06af\u06cc\u0631\u062f.<\/span><\/p>\r\n<p><a href=\"http:\/\/bloodhound1.efar.co.uk\/project\/car\/aerodynamics\/computational-fluid-dynamics\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10447 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/navier-stocks-equations.jpg\" alt=\"http:\/\/bloodhound1.efar.co.uk\/project\/car\/aerodynamics\/computational-fluid-dynamics\" width=\"400\" height=\"298\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/navier-stocks-equations.jpg 400w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/navier-stocks-equations-300x224.jpg 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2020\/12\/navier-stocks-equations-360x268.jpg 360w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\r\n<h3>\u00a0<\/h3>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #800000;\"><strong>\u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0631\u06af\u0631\u0632 (Burgers Equation)<\/strong><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0627\u06a9\u0646\u0648\u0646\u060c \u0628\u0627 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0633\u0627\u062f\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 (\u0647\u0630\u0644\u0648\u0644\u0648\u06cc)\u060c \u0644\u0627\u067e\u0644\u0627\u0633 (\u0628\u06cc\u0636\u0648\u06cc) \u0648 \u062a\u0648\u0632\u06cc\u0639 \u06af\u0631\u0645\u0627 (\u0633\u0647\u0645\u0648\u06cc) \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645. \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0627\u0633\u062a \u06a9\u0647 \u062a\u0631\u06a9\u06cc\u0628 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0647 \u0646\u062d\u0648\u06cc \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0627\u06a9\u0645 \u0628\u0631 \u062c\u0631\u06cc\u0627\u0646 \u0633\u06cc\u0627\u0644 (\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633) \u0645\u0633\u062a\u062a\u0631 \u0627\u0633\u062a. \u0645\u062b\u0644\u0627\u064b \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0642\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u062d\u0631\u06a9\u062a \u062e\u0637\u06cc \u062f\u0631 \u062c\u0647\u062a x (\u0645\u0639\u0627\u062f\u0644\u0647 ) \u062a\u0648\u062c\u0647 \u0646\u0645\u0627\u0626\u06cc\u062f.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-12079 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/11\/Burgers-Equation.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0631\u06af\u0631\u0632\" width=\"969\" height=\"213\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/11\/Burgers-Equation.png 969w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/11\/Burgers-Equation-300x66.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/11\/Burgers-Equation-768x169.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/11\/Burgers-Equation-360x79.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/11\/Burgers-Equation-600x132.png 600w\" sizes=\"auto, (max-width: 969px) 100vw, 969px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u062a\u0648\u062c\u0647 \u0634\u0648\u062f \u06a9\u0647 \u062a\u0631\u0645\u200c\u0647\u0627\u06cc (1) \u0648 (2) \u0648 \u06cc\u0627 (1) \u0648 (3) \u0645\u0634\u0627\u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u0628\u062a\u0647 \u0627\u0648\u0644\u060c \u062a\u0631\u0645\u200c\u0647\u0627\u06cc (1) \u0648 (5) \u0648 \u06cc\u0627 (1) \u0648 (6) \u0645\u0634\u0627\u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u062a\u0648\u0632\u06cc\u0639 \u06af\u0631\u0645\u0627 \u0648 \u062a\u0631\u0645\u200c\u0647\u0627\u06cc (5) \u0648 (6) \u0645\u0634\u0627\u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0644\u0627\u067e\u0644\u0627\u0633 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0644\u0630\u0627\u060c \u0645\u0644\u0627\u062d\u0638\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631 \u0627\u0633\u062a\u0648\u06a9\u0633 (\u06a9\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0622\u0646\u200c\u0647\u0627 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0642\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u062d\u0631\u06a9\u062a \u062e\u0637\u06cc \u0627\u0633\u062a) \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u0631\u0641\u062a\u0627\u0631\u0647\u0627\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc\u060c \u0633\u0647\u0645\u0648\u06cc \u0648 \u0628\u06cc\u0636\u0648\u06cc (Mixed Behavier) \u0631\u0627 \u062f\u0627\u0631\u062f. \u0627\u0632 \u0622\u0646\u062c\u0627\u0626\u06cc\u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631 \u0627\u0633\u062a\u0648\u06a9\u0633 \u062e\u06cc\u0644\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0647\u0633\u062a\u0646\u062f\u060c \u0628\u0639\u0636\u0627\u064b \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0622\u0646\u200c\u0647\u0627 \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0631\u06af\u0631 \u06a9\u0647 \u0641\u0631\u0645 \u0633\u0627\u062f\u0647 \u0634\u062f\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0646\u0627\u0648\u06cc\u0631 \u0627\u0633\u062a\u0648\u06a9\u0633 \u0627\u0633\u062a (\u062a\u0631\u0645 \u0641\u0634\u0627\u0631 \u0628\u0631\u0627\u0628\u0631 \u0635\u0641\u0631 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0647 \u0634\u062f\u0647) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0631\u06af\u0631 \u0644\u0632\u062c \u062f\u0648 \u0628\u0639\u062f\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (22) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062a\u0639\u062f\u062f\u06cc \u0628\u0631\u0627\u06cc \u062d\u0644 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u0634\u062f\u0647 \u06a9\u0647 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d FTCS\u060c FTBCS (\u067e\u06cc\u0634\u0631\u0648 \u062f\u0631 \u0632\u0645\u0627\u0646\u060c \u067e\u0633\u0631\u0648 \u062f\u0631 \u0645\u06a9\u0627\u0646 \u0628\u0631\u0627\u06cc \u062a\u0631\u0645\u200c\u0647\u0627\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0648 \u0645\u0631\u06a9\u0632\u06cc \u062f\u0631 \u0645\u06a9\u0627\u0646 \u0628\u0631\u0627\u06cc \u062a\u0631\u0645\u200c\u0647\u0627\u06cc \u0628\u06cc\u0636\u0648\u06cc)\u060c \u062f\u0648\u0641\u0648\u0631\u062a \u0641\u0631\u0627\u0646\u06a9\u0644\u060c \u0645\u06a9 \u06a9\u0648\u0631\u0645\u06a9 \u0648 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0636\u0645\u0646\u06cc \u0645\u06a9 \u06a9\u0648\u0631\u0645\u06a9\u060c BTCS \u0648 BTBS \u0627\u0632 \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0627\u06cc\u0646 \u0646\u0648\u0639 \u0631\u0648\u0634\u200c\u0647\u0627 \u0628\u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\">\u00a0<\/p>\r\n<p>&nbsp;<\/p>\r\n<h4 style=\"text-align: right;\">1- <a href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/finite-difference-method\/\"><span style=\"color: #3366ff;\"><strong>\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><\/span><\/a><\/h4>\r\n<h5 style=\"text-align: right;\"><span style=\"color: #000000;\"><strong>2- \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u062d\u062c\u0645 \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><\/span><\/h5>\r\n<h5 style=\"text-align: right;\"><span style=\"color: #000000;\"><strong>3- \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0627\u0644\u0645\u0627\u0646 \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><\/span><\/h5>\r\n<p>&nbsp;<\/p>\r\n\r\n<p class=\"has-text-align-left has-cyan-bluish-gray-color has-text-color wp-block-paragraph\" style=\"font-size: 18px;\"><strong>\u0627\u062f\u0627\u0645\u0647 \u062f\u0627\u0631\u062f\u2026<\/strong><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-right has-vivid-cyan-blue-color has-text-color wp-block-paragraph\" style=\"font-size: 18px;\"><span style=\"color: #3366ff;\"><strong><a style=\"color: #3366ff;\" href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/\">\u0628\u0627\u0632\u06af\u0634\u062a<\/a><\/strong><\/span><\/p>\r\n\r\n\r\n<hr \/>\r\n<h3 class=\"has-text-align-right has-vivid-red-color has-cyan-bluish-gray-background-color has-text-color has-background has-medium-font-size\" style=\"text-align: right;\"><span style=\"color: #800000;\"><strong>\u0645\u0637\u0627\u0644\u0628 \u0645\u0631\u062a\u0628\u0637<\/strong><\/span><\/h3>\r\n<hr \/>\r\n\r\n\r\n<h4 class=\"has-text-align-right has-black-color has-text-color\" style=\"text-align: right;\"><span style=\"color: #3366ff;\">1- <a style=\"color: #3366ff;\" href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/finite-difference-method\/hyperbolic-pde\/\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c)<\/strong><\/a><\/span><\/h4>\r\n<h4 class=\"page-title\" style=\"text-align: right;\"><span style=\"color: #3366ff;\">2- <a style=\"color: #3366ff;\" href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/elliptic-pdes\/\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \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)<\/strong><\/a><\/span><\/h4>\r\n<h4 style=\"text-align: right;\"><span style=\"color: #3366ff;\">3- <a style=\"color: #3366ff;\" href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/parabolic-pdes\/\"><strong>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc (\u0645\u0639\u0627\u062f\u0644\u0647 \u062a\u0648\u0632\u06cc\u0639 \u06af\u0631\u0645\u0627)<\/strong><\/a><\/span><\/h4>\r\n<p class=\"has-text-align-left has-cyan-bluish-gray-color has-text-color wp-block-paragraph\" style=\"font-size: 18px; text-align: left;\"><span style=\"color: #999999;\"><em><a style=\"color: #999999;\" href=\"https:\/\/cfd-mrk.ir\/index.php\/contact-us\/\"><strong>\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><\/p>\r\n<h4 style=\"text-align: left;\"><a href=\"http:\/\/ae.sharif.edu\/~portal\/faculty\/2084842152\"><em><span style=\"color: #0000ff;\"><strong>\u062f\u06a9\u062a\u0631 \u0645\u062d\u0645\u062f \u0637\u06cc\u0628\u06cc \u0631\u0647\u0646\u06cc<\/strong><\/span><\/em><\/a><\/h4>\r\n\r\n\r\n\r\n<h4 class=\"has-text-align-left has-text-color\" style=\"color: #0006a3; text-align: left;\"><span style=\"color: #0000ff;\"><strong><em><a style=\"color: #0000ff;\" href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/mohammad-reza-kelich-cv\/\">\u0645\u062d\u0645\u062f\u0631\u0636\u0627 \u06a9\u0644\u06cc\u0686<\/a><\/em><\/strong><\/span><\/h4>\r\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc Partial Differential Equation \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a\u06cc \u06af\u0641\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0622\u0646 \u062a\u0627\u0628\u0639 \u062f\u0648 \u06cc\u0627 \u0686\u0646\u062f \u0645\u062a\u063a\u06cc\u0631 \u0645\u0633\u062a\u0642\u0644 \u0628\u0648\u062f\u0647 \u06a9\u0647 \u0628\u0647 \u0634\u06a9\u0644 \u062a\u0631\u0645\u0647\u0627\u06cc \u0645\u0634\u062a\u0642\u06cc \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0638\u0627\u0647\u0631 \u0634\u062f\u0647 \u0628\u0627\u0634\u062f. \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0635\u0648\u0631\u062a\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641&hellip;&nbsp;<a href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/\" class=\"more-link\">Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":10404,"parent":3477,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-10401","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u0644 \u062c\u0632\u0626\u06cc - cfd-mrk<\/title>\n<meta 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