{"id":32826,"date":"2020-08-15T19:59:59","date_gmt":"2020-08-15T16:59:59","guid":{"rendered":"http:\/\/ihcoedu.uobaghdad.edu.iq\/?p=32826"},"modified":"2020-09-20T10:55:04","modified_gmt":"2020-09-20T07:55:04","slug":"%d9%82%d8%b3%d9%85-%d8%a7%d9%84%d8%b1%d9%8a%d8%a7%d8%b6%d9%8a%d8%a7%d8%aa-%d9%8a%d9%86%d8%a7%d9%82%d8%b4-%d8%b1%d8%b3%d8%a7%d9%84%d8%a9-%d9%85%d8%a7%d8%ac%d8%b3%d8%aa%d9%8a%d8%b1-%d8%aa%d8%a8%d8%ad-5","status":"publish","type":"post","link":"https:\/\/ihcoedu.uobaghdad.edu.iq\/?p=32826","title":{"rendered":"\u0642\u0633\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u064a\u0646\u0627\u0642\u0634 \u0631\u0633\u0627\u0644\u0629 \u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u062a\u0628\u062d\u062b \u0641\u064a \u0627\u0644\u062d\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0644\u0644\u0634\u0643\u0644 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0641\u064a \u0628\u0639\u062f\u064a\u0646 \u0645\u0643\u0627\u0646\u064a\u064a\u0646"},"content":{"rendered":"

\"\"\u00a0<\/strong><\/span><\/h4>\n

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    \n
  • \n

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  • \n

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  • \n

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  • \n

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  • \n

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    \u00a0<\/strong><\/span><\/h4>\n

    \u0648<\/strong>\u062a\u0647\u062f\u0641 \u0647\u0630\u0647 \u0627\u0644\u0631\u0633\u0627\u0644\u0629 \u0625\u0644\u0649 \u0645\u0646\u0627\u0642\u0634\u0629 \u0627\u0644\u062d\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0641\u064a \u0628\u0639\u062f\u064a\u0646 \u0645\u0643\u0627\u0646\u064a\u064a\u0646 \u0641\u064a \u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a (\u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 \u0627\u0644\u0635\u062d\u064a\u062d\u0629) \u0648\u0643\u0630\u0644\u0643 \u0641\u064a \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0643\u0633\u0631\u064a (\u0645\u0639 \u0645\u0634\u062a\u0642 \u0627\u0644\u0632\u0645\u0646 \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 \u0627\u0644\u0643\u0633\u0631\u064a\u0629).<\/span><\/h4>\n

    \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0641\u064a \u0634\u0643\u0644\u0647\u0627 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a \u0641\u0627\u0646\u0646\u0627 \u0642\u062f\u0645\u0646\u0627 \u062a\u062d\u0633\u064a\u0646\u0627 \u0639\u0644\u0649 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u0646\u0627\u0648\u0628 \u0627\u0644\u0636\u0645\u0646\u064a (Alternating Direction Implicit method) \u0644\u0646\u062d\u0635\u0644 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0627 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0639\u0644\u0649 \u0635\u064a\u063a\u0629 \u0645\u0643\u0627\u0641\u0626\u0629 \u0644\u0635\u064a\u063a\u0629 \u0643\u0631\u0627\u0646\u0643 \u0648\u0646\u064a\u0643\u0644\u0633\u0648\u0646 (Crank – Nicolson) \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u062f\u0642\u0629 \u0648\u062e\u0637\u0623 \u0627\u0644\u0642\u0637\u0639 \u0648\u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u0648\u0642\u062a \u062a\u0645\u062a\u0644\u0643 \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0627\u0644\u062c\u064a\u062f\u0629 \u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u0646\u0627\u0648\u0628 \u0627\u0644\u0636\u0645\u0646\u064a \u0628\u0627\u0644\u0627\u0636\u0627\u0641\u0629 \u0627\u0644\u0649 \u0643\u0648\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0645\u0633\u062a\u0642\u0631\u0629 \u0628\u062f\u0648\u0646 \u0634\u0631\u0648\u0637 \u0645\u062b\u0644 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u0646\u0627\u0648\u0628 \u0627\u0644\u0636\u0645\u0646\u064a \u0648\u064a\u0645\u0643\u0646 \u062d\u0644\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0634\u0627\u0628\u0647\u0629 \u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0645\u062a\u0646\u0627\u0648\u0628 \u0627\u0644\u0636\u0645\u0646\u064a \u0645\u0639 \u0628\u0639\u0636 \u0627\u0644\u062a\u0639\u062f\u064a\u0644\u0627\u062a.<\/span><\/h4>\n

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    \n

    Numerical Solution for Two Dimensional Fractional Heat Equation<\/span><\/h3>\n

    By Isra’a .A.Ibrahim<\/span><\/h3>\n

    Supervised by Asst. Prof. Dr. Salwa Salman Abed<\/span><\/h3>\n

    Abstract<\/span><\/h3>\n

    This thesis aims to discuss the numerical solution of two-dimensional diffusion equation in the classical form (the integer order derivative) and with the fractional form (with fractional order derivative in the time-fractional diffusion equation\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><\/h3>\n

    For the classical form we introduce an improvement to the Alternating Direction Implicit method and get an equivalent scheme to Crank – Nicolson differences scheme in two dimensions. This improvement have the same main good feature of the Alternating Direction Implicit method with more accurate resuits.\u00a0 It is also unconditionally stable like the Alternating Direction Implicit\u00a0 method and can be solved by similar Alternating Direction Implicit\u00a0 algorithm with some modification\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\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\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/h3>\n

    The suggested method has been used to solve the standard diffusion equation in two dimension but it can be used for any other partial differential equation with more one dimension instead of the Alternating Direction Implicit method<\/span><\/h3>\n

    For the fractional case we use the Caputo definition of fractional derivative for the time derivative of diffusion equation. The fractional scheme will be a multi level scheme due to memory and hereditary properties of the time fractional derivative. The stability condition obtained by reformulation the classical multilevel technique on the finite difference scheme to be suitable for the time fractional case.<\/span><\/h3>\n

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

    \u00a0 \u0646\u0627\u0642\u0634 \u0642\u0633\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0641\u064a \u0643\u0644\u064a\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0629 \u0644\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0635\u0631\u0641\u0629 ( \u0627\u0628\u0646 \u0627\u0644\u0647\u064a\u062b\u0645 ) \u0631\u0633\u0627\u0644\u0629 \u0627\u0644\u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u0627\u0644\u0645\u0648\u0633\u0648\u0645\u0629 ( \u0627\u0644\u062d\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0644\u0645\u0639\u0627\u062f\u0644\u0629….<\/i>\u0627\u0644\u0645\u0632\u064a\u062f<\/span><\/a><\/p>\n","protected":false},"author":25,"featured_media":32829,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"categories":[7,16],"tags":[23,49],"class_list":["post-32826","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7","category-16","tag-ihcoedu","tag-math"],"modified_by":"ihcoedu","_links":{"self":[{"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=\/wp\/v2\/posts\/32826","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=\/wp\/v2\/users\/25"}],"replies":[{"embeddable":true,"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=32826"}],"version-history":[{"count":0,"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=\/wp\/v2\/posts\/32826\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=\/wp\/v2\/media\/32829"}],"wp:attachment":[{"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32826"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32826"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ihcoedu.uobaghdad.edu.iq\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}