{"id":11412,"date":"2021-09-28T19:43:00","date_gmt":"2021-09-28T16:13:00","guid":{"rendered":"https:\/\/cfd-mrk.ir\/?page_id=11412"},"modified":"2021-11-22T09:35:42","modified_gmt":"2021-11-22T06:05:42","slug":"hyperbolic-pde","status":"publish","type":"page","link":"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/finite-difference-method\/hyperbolic-pde\/","title":{"rendered":"\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc"},"content":{"rendered":"\r\n<h2 class=\"has-text-align-right has-black-color has-text-color wp-block-heading\" style=\"text-align: right;\"><span style=\"color: #000000;\"><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><\/span><\/h2>\r\n\r\n\r\n\r\n<h2 class=\"has-text-align-left has-black-color has-text-color wp-block-heading\" style=\"text-align: left;\"><span style=\"color: #000000;\"><strong>Numerical Solution of Hyperbolic Partial Equations by Finite Difference Method<\/strong><\/span><\/h2>\r\n<p class=\"has-text-align-right has-black-color has-text-color\" style=\"text-align: right;\"><span style=\"color: #000000;\">\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0634\u062a\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0647 \u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631\u060c <\/span><span style=\"color: #000000;\">\u062f\u0633\u062a\u0647 \u062e\u0627\u0635\u06cc \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u06a9\u0647 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u0639\u0631\u0648\u0641 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u062f\u0631 \u0627\u06cc\u0646 \u067e\u0633\u062a \u0645\u0648\u0631\u062f \u0628\u0631\u0631\u0633\u06cc \u0642\u0631\u0627\u0631 \u06af\u0631\u0641\u062a\u0647 \u0627\u0633\u062a. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631<a href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/\"><span style=\"color: #3366ff;\"><strong> \u0627\u06cc\u0646\u062c\u0627<\/strong><\/span><\/a> \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u0647\u060c \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0646\u0627\u0648\u06cc\u0631-\u0627\u0633\u062a\u0648\u06a9\u0633 \u0633\u0647 \u062f\u0633\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u0633\u0647\u0645\u0648\u06cc\u060c \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0648 \u0628\u06cc\u0636\u0648\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0633\u062a\u0647 \u0628\u0647 \u0645\u0627\u0647\u06cc\u062a \u062c\u0631\u06cc\u0627\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0633\u0647 \u062f\u0633\u062a\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0639\u0646\u0648\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u063a\u0627\u0644\u0628 \u0638\u0627\u0647\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0627\u06a9\u0645 \u0628\u0631 \u062c\u0631\u06cc\u0627\u0646\u0647\u0627\u06cc \u0645\u0627\u0641\u0648\u0642 \u0635\u0648\u062a\u060c \u063a\u06cc\u0631 \u0644\u0632\u062c \u0648 \u067e\u0627\u06cc\u0627 \u062c\u0632\u0621 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <strong>\u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c<\/strong> \u0628\u0627\u0631\u0632\u062a\u0631\u06cc\u0646 \u0646\u0645\u0648\u0646\u0647 \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 \u0628\u0634\u0645\u0627\u0631 \u0645\u06cc\u200c\u0631\u0648\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628 \u067e\u0633 \u0627\u0632 \u0645\u0639\u0631\u0641\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0648 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0622\u0646 \u0627\u0632 \u0644\u062d\u0627\u0638 \u0645\u0631\u062a\u0628\u0647 \u0648 \u0631\u0641\u062a\u0627\u0631 (\u0627\u06cc\u0646\u06a9\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0627\u0633\u062a)\u060c \u0628\u0647 \u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0622\u0646 \u0646\u06cc\u0632 \u0627\u0634\u0627\u0631\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0647\u0645\u0686\u0646\u06cc\u0646\u060c \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0648 \u062f\u0648\u0645 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0648 \u0627\u0646\u0648\u0627\u0639 \u0645\u062a\u062f\u0647\u0627\u06cc \u0635\u0631\u06cc\u062d \u0648 \u0636\u0645\u0646\u06cc \u0645\u0639\u0631\u0641\u06cc \u0648 \u00a0\u067e\u0627\u06cc\u062f\u0627\u0631\u06cc \u0622\u0646\u0647\u0627 \u0628\u0631\u0631\u0633\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\r\n<h3>\u00a0<\/h3>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc61605242\"><\/a><span style=\"color: #800000;\"><strong>\u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c<\/strong><\/span><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 (1) \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc \u062e\u0637\u06cc \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u0646\u06cc\u0632 \u0645\u0639\u0631\u0641\u06cc \u0645\u06cc\u200c\u0634\u0648\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0630\u06a9\u0648\u0631 \u0628\u06cc\u0627\u0646\u06af\u0631 \u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0645\u0648\u0627\u062c\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0627 \u0633\u0631\u0639\u062a <strong><em>c<\/em><\/strong> \u0648 \u0628\u0637\u0648\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0645\u0646\u062a\u0634\u0631 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 (1) \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 (\u0645\u0639\u0627\u062f\u0644\u0647 2) \u0646\u06cc\u0632 \u0646\u0648\u0634\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (2) \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0647 (1) \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f. \u062f\u0631 \u062d\u0642\u06cc\u0642\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a (2) \u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f \u06a9\u0647 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627\u06cc\u06cc \u0634\u0628\u06cc\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (1) \u062f\u0627\u0631\u062f. \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646\u06a9\u0647 <strong><em>u=f(x,t)<\/em><\/strong> \u0648 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0642\u0627\u0646\u0648\u0646 \u0632\u0646\u062c\u06cc\u0631\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 (3) \u0631\u0627 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0646\u0645\u0648\u062f.<\/span><span style=\"color: #000000; font-size: 9pt;\"> \u062a\u0631\u06a9\u06cc\u0628 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (2) \u0648 (3) \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (4) \u0631\u0627 \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc\u200c\u062f\u0647\u062f. \u0628\u0627 \u0635\u0641\u0631 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0646 \u062f\u062a\u0631\u0645\u06cc\u0646\u0627\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0636\u0631\u0627\u0626\u0628 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0630\u06a9\u0648\u0631 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0631\u0627\u0628\u0637\u0647 (5) \u0631\u0633\u06cc\u062f.<\/span><\/p>\r\n<h5>\u00a0<\/h5>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 (\u0645\u0639\u0627\u062f\u0644\u06476) \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u0645\u0634\u062e\u0635\u0647 \u062d\u0642\u06cc\u0642\u06cc <strong><em>(dx\/dt=c)<\/em><\/strong> \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f (\u0634\u06a9\u0644 1). \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 (2)\u060c \u06a9\u0647 \u0628\u0647 \u0646\u0648\u0639\u06cc \u0628\u06cc\u0627\u0646\u06af\u0631 \u0631\u0641\u062a\u0627\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u06cc\u200c\u0628\u0627\u0634\u062f\u060c \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u062e\u0637\u06cc \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0645\u0648\u062c\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0627 \u0633\u0631\u0639\u062a <strong><em>c<\/em><\/strong><strong><em>\u00b1<\/em><\/strong> \u062f\u0631 \u062c\u0647\u062a\u200c\u0647\u0627\u06cc \u0645\u062b\u0628\u062a \u0648 \u0645\u0646\u0641\u06cc <strong><em>x<\/em><\/strong> \u062f\u0631 \u0635\u0641\u062d\u0647 <strong><em>(<\/em><\/strong><strong><em>x, t<\/em><\/strong><strong><em>)<\/em><\/strong> \u0627\u0646\u062a\u0634\u0627\u0631 \u0645\u06cc\u200c\u06cc\u0627\u0628\u062f (\u0634\u06a9\u0644 2). \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u060c \u0645\u0634\u062e\u0635\u0627\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0630\u06a9\u0648\u0631 \u062f\u0631 \u0646\u0642\u0637\u0647 <strong><em>p<\/em><\/strong> \u0628\u0635\u0648\u0631\u062a \u0634\u06a9\u0644 (2) \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-11431 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c\" width=\"1040\" height=\"515\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation.png 1040w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-300x149.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-1024x507.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-768x380.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-360x178.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-600x297.png 600w\" sizes=\"auto, (max-width: 1040px) 100vw, 1040px\" \/><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-11432 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/characteristic-lines.png\" alt=\"\u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c\" width=\"1059\" height=\"472\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/characteristic-lines.png 1059w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/characteristic-lines-300x134.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/characteristic-lines-1024x456.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/characteristic-lines-768x342.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/characteristic-lines-360x160.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/characteristic-lines-600x267.png 600w\" sizes=\"auto, (max-width: 1059px) 100vw, 1059px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0627\u0632 \u0634\u06a9\u0644\u200c\u0647\u0627\u06cc (1) \u0648 (2) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u06cc\u0646\u06af\u0648\u0646\u0647 \u0627\u0633\u062a\u0646\u0628\u0627\u0637 \u06a9\u0631\u062f \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c\u060c \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u0628\u0647 \u062d\u0644 \u0645\u062d\u0644\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0646\u0628\u0648\u062f\u0647 \u0648 \u0628\u0635\u0648\u0631\u062a \u062e\u0637 \u0631\u0627\u0633\u062a \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0634\u06a9\u0644 (2) \u0646\u0627\u062d\u06cc\u0647 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0631\u0627 \u0628\u0647 \u0633\u0647 \u062f\u0627\u0645\u0646\u0647 \u0633\u06a9\u0648\u062a(Domain of Silence) \u060c \u062a\u0623\u062b\u06cc\u0631 \u06af\u0630\u0627\u0631(Domain of Influence) \u0648 \u0648\u0627\u0628\u0633\u062a\u0647(Domain of Dependence) \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0627\u0644\u0628\u062a\u0647 \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u062f\u0631 \u0628\u0631\u062e\u06cc \u0645\u0633\u0627\u0626\u0644 \u0628\u0647 \u062d\u0644 \u0645\u062d\u0644\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a \u0648 \u0627\u0646\u062d\u0646\u0627 \u062f\u0627\u0631\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 \u062c\u0631\u06cc\u0627\u0646 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u062a\u0631\u0627\u06a9\u0645\u200c\u067e\u0630\u06cc\u0631 \u062f\u0648 \u0628\u0639\u062f\u06cc \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u0633\u0627\u0633 \u0645\u0624\u0644\u0641\u0647\u200c\u0647\u0627\u06cc \u0633\u0631\u0639\u062a\u060c \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0627\u062a (7) \u0648 (8) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u06a9\u0631\u062f. \u0628\u0631\u0627\u06cc \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0630\u06a9\u0648\u0631 \u062f\u0648 \u0645\u0642\u062f\u0627\u0631 \u0645\u0634\u062e\u0635\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0634\u06cc\u0628 \u0622\u0646\u0647\u0627 \u0628\u0631\u0627\u0633\u0627\u0633 \u0631\u0627\u0628\u0637\u0647 (9) \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-11439 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/nonlinear-characteristic-lines.png\" alt=\"\u0645\u0639\u0627\u062f\u0644\u0647 \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c\" width=\"1029\" height=\"328\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/nonlinear-characteristic-lines.png 1029w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/nonlinear-characteristic-lines-300x96.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/nonlinear-characteristic-lines-1024x326.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/nonlinear-characteristic-lines-768x245.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/nonlinear-characteristic-lines-360x115.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/nonlinear-characteristic-lines-600x191.png 600w\" sizes=\"auto, (max-width: 1029px) 100vw, 1029px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0627\u0632 \u0622\u0646\u062c\u0627 \u06a9\u0647 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (9) <strong><em>dy\/dx<\/em><\/strong> \u0628\u0647 <strong><em>u<\/em><\/strong> \u0648 <strong><em>v<\/em><\/strong> \u0648\u0627\u0628\u0633\u062a\u0647 \u0628\u0648\u062f\u0647 \u0648 \u0627\u06cc\u0646 \u062f\u0648 \u06a9\u0645\u06cc\u062a \u0646\u06cc\u0632 \u062a\u0627\u0628\u0639\u06cc \u0627\u0632 \u0645\u06a9\u0627\u0646 \u0627\u0633\u062a\u060c \u0644\u0630\u0627 \u062e\u0637\u0648\u0637 \u0645\u0634\u062e\u0635\u0647 \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0647 \u062d\u0644 \u0645\u062d\u0644\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0628\u0648\u062f\u0647 \u0648 \u0627\u0646\u062d\u0646\u0627 \u062f\u0627\u0631\u062f [1].<\/span><\/p>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc61605243\"><\/a><span style=\"color: #800000;\"><strong>\u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c<\/strong><\/span><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0645\u0646\u0638\u0648\u0631 \u062f\u0631\u06a9 \u0628\u0647\u062a\u0631 \u0648 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u0628\u0627 \u0631\u0648\u0634 \u062a\u062d\u0644\u06cc\u0644\u06cc\u060c \u062f\u0631 \u0627\u06cc\u0646 \u062c\u0627 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0628\u0637\u0648\u0631 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0648 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634 \u062f\u0622\u0644\u0645\u0628\u0631\u062a (D&#8217;Alembert) \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f[2]. \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10) \u0628\u06cc\u0627\u0646\u06af\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0645\u0631\u062a\u0628\u0647 \u062f\u0648 \u0648 \u0634\u0631\u0627\u0626\u0637 \u0627\u0648\u0644\u06cc\u0647 \u0622\u0646 \u0645\u06cc\u200c\u0628\u0627\u0634\u062f. \u0628\u0631\u0627\u06cc \u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0622\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u0632 \u0627\u0646\u062a\u0642\u0627\u0644 \u0641\u0648\u0631\u06cc\u0647 (\u0627\u0646\u062a\u0642\u0627\u0644 <strong><em>x<\/em><\/strong>) \u0648 \u06cc\u0627 \u0627\u0646\u062a\u0642\u0627\u0644 \u0644\u0627\u067e\u0644\u0627\u0633 (\u0627\u0646\u062a\u0642\u0627\u0644 <strong><em>t<\/em><\/strong>) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. \u062f\u0631 \u0647\u0645\u06cc\u0646 \u0631\u0627\u0633\u062a\u0627\u060c \u0633\u06cc\u0633\u062a\u0645 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10) \u062f\u0631 \u0637\u06cc \u0645\u0631\u0627\u062d\u0644 \u0632\u06cc\u0631 \u062d\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\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 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>\r\n<h4 style=\"text-align: right;\"><span style=\"color: #ff0000;\"><strong>\u0645\u0631\u062d\u0644\u0647 \u0627\u0648\u0644: \u062a\u063a\u06cc\u06cc\u0631 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc <\/strong><strong><em>(x,t)<\/em><\/strong><strong> \u0628\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc <\/strong><strong><em>(<\/em><\/strong><strong><em>\u03be,\u03b7<\/em><\/strong><strong><em>)<\/em><\/strong><\/span><\/h4>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0631\u0627\u06cc \u062d\u0644 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10)\u060c \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 <strong><em>(x,t)<\/em><\/strong> \u0628\u0627 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u0645\u06a9\u0627\u0646\u06cc-\u0632\u0645\u0627\u0646\u06cc\u060c<strong><em>(<\/em><\/strong><strong><em>\u03be,<\/em><\/strong><strong><em>\u03b7<\/em><\/strong><strong><em>)<\/em><\/strong> \u00a0\u0648 \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (11) \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f. \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \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\u0639\u0627\u062f\u0644\u0647 (12) \u062d\u0627\u0635\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f. \u0628\u0627 \u0642\u0631\u0627\u0631 \u062f\u0627\u062f\u0646 \u0631\u0648\u0627\u0628\u0637 (12) \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c (\u0631\u0627\u0628\u0637\u0647 \u0627\u0648\u0644 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a10) \u0631\u0627\u0628\u0637\u0647 (13) \u0646\u062a\u06cc\u062c\u0647 \u06af\u0631\u0641\u062a\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-11441 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-1.png\" alt=\"\u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c-1\" width=\"1028\" height=\"444\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-1.png 1028w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-1-300x130.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-1-1024x442.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-1-768x332.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-1-360x155.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-1-600x259.png 600w\" sizes=\"auto, (max-width: 1028px) 100vw, 1028px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\"><strong>\u00a0<\/strong><\/span><\/p>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #000000;\"><strong>\u00a0<\/strong><\/span><span style=\"color: #ff0000;\"><strong>\u0645\u0631\u062d\u0644\u0647 \u062f\u0648\u0645: \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0646\u062a\u0642\u0627\u0644 \u06cc\u0627\u0641\u062a\u0647<\/strong><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0631\u0648\u0627\u0628\u0637 (12) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u067e\u06cc \u0628\u0631\u062f \u06a9\u0647 \u062a\u0627\u0628\u0639 <strong><em>u(\u03be,\u03b7)<\/em><\/strong> \u062d\u062a\u0645\u0627\u064b \u0628\u0627\u06cc\u062f \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0627\u0632 \u062f\u0648 \u062a\u0627\u0628\u0639 \u062a\u06a9 \u0645\u062a\u063a\u06cc\u0631\u0647 <strong><em>\u03be<\/em><\/strong> \u0648 <strong><em>\u03b7<\/em><\/strong> \u0628\u0627\u0634\u062f \u0648 \u062f\u0631 \u0646\u062a\u06cc\u062c\u0647 \u0631\u0627\u0628\u0637\u0647 (14) \u062f\u0631 \u062f\u0633\u062a\u06af\u0627\u0647 \u0627\u0646\u062a\u0642\u0627\u0644 \u06cc\u0627\u0641\u062a\u0647 \u062d\u0627\u06a9\u0645 \u0627\u0633\u062a:<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-11447 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-2.png\" alt=\"\u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c\" width=\"1015\" height=\"49\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-2.png 1015w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-2-300x14.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-2-768x37.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-2-360x17.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-2-600x29.png 600w\" sizes=\"auto, (max-width: 1015px) 100vw, 1015px\" \/><\/p>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\"><strong><em>\u03d5(\u03b7)<\/em><\/strong> \u0648 <strong><em>\u03c8(\u03be)<\/em><\/strong> \u062a\u0648\u0627\u0628\u0639 \u062f\u0644\u062e\u0648\u0627\u0647\u06cc \u0627\u0632 <strong><em>\u03b7<\/em><\/strong> \u0648 <strong><em>\u03be<\/em><\/strong> \u0645\u06cc\u200c\u0628\u0627\u0634\u062f.<\/span><\/p>\r\n<p>&nbsp;<\/p>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #ff0000;\"><strong>\u0645\u0631\u062d\u0644\u0647 \u0633\u0648\u0645: \u0628\u0627\u0632\u06af\u0634\u062a \u0628\u0647 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u062e\u062a\u0635\u0627\u062a \u0627\u0635\u0644\u06cc<\/strong><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u067e\u0627\u0633\u062e \u06a9\u0644\u06cc \u0628\u0631\u0627\u06cc \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10)\u060c \u06a9\u0627\u0641\u06cc\u0633\u062a \u06a9\u0647 \u0631\u0648\u0627\u0628\u0637 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f\u06cc \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (11) \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 (14) \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u0634\u0648\u062f. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u067e\u0627\u0633\u062e \u06a9\u0644\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u0647 (15) \u0645\u06cc\u200c\u0628\u0627\u0634\u062f:<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-11448 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-3.png\" alt=\"\u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c-3\" width=\"1017\" height=\"63\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-3.png 1017w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-3-300x19.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-3-768x48.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-3-360x22.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-3-600x37.png 600w\" sizes=\"auto, (max-width: 1017px) 100vw, 1017px\" \/><\/p>\r\n<p>&nbsp;<\/p>\r\n<h3 style=\"text-align: right;\"><span style=\"color: #ff0000;\"><strong>\u0645\u0631\u062d\u0644\u0647 \u0686\u0647\u0627\u0631\u0645: \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u067e\u0627\u0633\u062e \u06a9\u0644\u06cc \u062f\u0631 \u0634\u0631\u0627\u0626\u0637 \u0627\u0648\u0644\u06cc\u0647<\/strong><\/span><\/h3>\r\n<p style=\"text-align: right;\"><span style=\"color: #000000;\">\u067e\u0633 \u0627\u0632 \u062f\u0633\u062a\u06cc\u0627\u0628\u06cc \u0628\u0647 \u067e\u0627\u0633\u062e \u06a9\u0644\u06cc \u0648 \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u062f\u0631 \u0634\u0631\u0627\u0626\u0637 \u0627\u0648\u0644\u06cc\u0647 (\u0645\u0639\u0627\u062f\u0644\u064710) \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (16) \u0631\u0633\u06cc\u062f. \u0628\u0627 \u0627\u0646\u062a\u06af\u0631\u0627\u0644 \u06af\u06cc\u0631\u06cc \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 \u062f\u0648\u0645 \u0645\u0639\u0627\u062f\u0644\u0647 (16)\u060c \u062a\u0648\u0627\u0628\u0639 \u00a0\u0648 \u00a0\u0628\u0647 \u0635\u0648\u0631\u062a \u0631\u0648\u0627\u0628\u0637 (17) \u0628\u0627\u0632\u0646\u0648\u06cc\u0633\u06cc \u0645\u06cc\u200c\u0634\u0648\u0646\u062f. \u062f\u0631 \u0646\u0647\u0627\u06cc\u062a \u062d\u0644 \u062f\u0642\u06cc\u0642 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0628\u0627 \u0634\u0631\u0627\u0626\u0637 \u0627\u0648\u0644\u06cc\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0634\u062f\u0647 \u062f\u0631 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u0639\u0627\u062f\u0644\u0627\u062a (10) \u0637\u0628\u0642 \u0645\u0639\u0627\u062f\u0644\u0647 (18) \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-11449 size-full\" src=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-4.png\" alt=\"\u062d\u0644 \u062a\u062d\u0644\u06cc\u0644\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c-4\" width=\"1037\" height=\"375\" srcset=\"https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-4.png 1037w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-4-300x108.png 300w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-4-1024x370.png 1024w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-4-768x278.png 768w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-4-360x130.png 360w, https:\/\/cfd-mrk.ir\/wp-content\/uploads\/2021\/09\/wave-equation-analytical-solution-4-600x217.png 600w\" sizes=\"auto, (max-width: 1037px) 100vw, 1037px\" \/><\/p>\r\n<ul style=\"text-align: right;\">\r\n<li><span style=\"color: #000000;\"><a style=\"color: #000000;\" name=\"_Toc61605244\"><\/a><span style=\"color: #000000;\">\u0645\u0639\u0627\u062f\u0644\u0647 (18) \u062d\u0644 \u062f\u0642\u06cc\u0642 \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0627\u0633\u062a. \u062f\u0631 \u0646\u0648\u0634\u062a\u0647\u200c\u0647\u0627\u06cc \u0622\u06cc\u0646\u062f\u0647 \u0645\u0642\u0627\u06cc\u0633\u0647 \u062d\u0644 \u062f\u0642\u06cc\u0642 \u0628\u0627 \u0631\u0648\u0634\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062d\u0644 \u0639\u062f\u062f\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u0645\u0648\u062c \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.\u00a0<\/span><\/span><\/li>\r\n<li><span style=\"color: #000000;\"><span style=\"color: #000000;\">\u00a0<\/span><\/span><\/li>\r\n<\/ul>\r\n<p>&nbsp;<\/p>\r\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><strong>:[1]<\/strong><\/span><\/p>\r\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><strong>K. A. Hoffman AND S.T. Chaing, \u201cComputational Fluid Dynamics for Engineer\u201d, Volume 1, Engineering Education System, Wichita, Kansas, 1993<\/strong><\/span><\/p>\r\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><strong>:[2]<\/strong><\/span><\/p>\r\n<p style=\"text-align: left;\"><span style=\"color: #000000;\"><strong> Stanley J. Farlow, &#8220;Partial Differential Equations for Scientists and engineers&#8221;, Dover Publications INC, New York, 1993<\/strong><\/span><\/p>\r\n<h4 class=\"has-text-align-right has-black-color has-text-color\" style=\"text-align: right;\"><a href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/solving-hyperbolic-pdes-using-fdm\/\"><span style=\"color: #3366ff;\"><strong>\u062d\u0644 \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) \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/span><\/a><\/h4>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<h3 class=\"has-text-align-right has-vivid-cyan-blue-color has-text-color\" style=\"text-align: right;\"><a href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/\"><span style=\"color: #3366ff;\"><strong>\u0628\u0627\u0632\u06af\u0634\u062a<\/strong><\/span><\/a><\/h3>\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<h4 style=\"text-align: right;\"><span style=\"color: #3366ff;\"><strong><a style=\"color: #3366ff;\" href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/\">\u0645\u0639\u0631\u0641\u06cc \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc<\/a><\/strong><\/span><\/h4>\r\n<h4 class=\"page-title\" style=\"text-align: right;\"><span style=\"color: #3366ff;\"><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;\"><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<h4 class=\"has-text-align-right has-black-color has-text-color\" style=\"text-align: right;\"><a href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/solving-hyperbolic-pdes-using-fdm\/\"><span style=\"color: #3366ff;\"><strong>\u062d\u0644 \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) \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f<\/strong><\/span><\/a><\/h4>\r\n<h4 class=\"has-text-align-left has-cyan-bluish-gray-color has-text-color\" style=\"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><\/h4>\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<h5 class=\"has-text-align-left has-text-color\" style=\"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><\/h5>\r\n","protected":false},"excerpt":{"rendered":"<p>\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) Numerical Solution of Hyperbolic Partial Equations by Finite Difference Method \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u06cc \u0647\u0630\u0644\u0648\u0644\u0648\u06cc \u0628\u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u062f\u0631 \u0627\u06cc\u0646 \u0646\u0648\u0634\u062a\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. \u0628\u0647 \u0639\u0628\u0627\u0631\u062a \u062f\u06cc\u06af\u0631\u060c \u062f\u0633\u062a\u0647 \u062e\u0627\u0635\u06cc \u0627\u0632 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062f\u06cc\u0641\u0631\u0627\u0646\u0633\u06cc\u0644 \u062c\u0632\u0626\u06cc \u06a9\u0647 \u0628\u0647&hellip;&nbsp;<a href=\"https:\/\/cfd-mrk.ir\/index.php\/training\/flow-analysis\/fundamentals-of-cfd\/partial-differential-equation\/finite-difference-method\/hyperbolic-pde\/\" class=\"more-link\">Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":11432,"parent":10820,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-11412","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u064a \u0647\u0630\u0644\u0648\u0644\u0648\u064a - cfd-mrk<\/title>\n<meta name=\"description\" content=\"\u062d\u0644 \u0639\u062f\u062f\u064a \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u064a \u0647\u0630\u0644\u0648\u0644\u0648\u064a \u0628\u0647 \u0631\u0648\u0634 \u062a\u0641\u0627\u0636\u0644 \u0645\u062d\u062f\u0648\u062f \u0628\u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u062f\u0631 \u0627\u06cc\u0646 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