{"id":43235,"date":"2026-08-13T05:47:16","date_gmt":"2026-08-13T05:47:16","guid":{"rendered":"https:\/\/uomosul.edu.iq\/en\/computerscience\/?p=43235"},"modified":"2026-08-13T05:47:16","modified_gmt":"2026-08-13T05:47:16","slug":"1-703","status":"publish","type":"post","link":"https:\/\/uomosul.edu.iq\/en\/computerscience\/2026\/08\/13\/1-703\/","title":{"rendered":"Doctoral Thesis by \u201c\u2019Mahmood Madian Abdullah AL-Zaidy\u201d"},"content":{"rendered":"<p><strong>Department of Mathematics<\/strong><\/p>\n<p>Discussion of the doctoral thesis at the College of Computer Science and Mathematics, Department of Mathematics, entitled:<\/p>\n<p><strong>\u201cImproving Wavelet Methods for Approximate Solutions of Nonlinear Partial Differential Equations\u201d<\/strong><\/p>\n<p>supervised by <strong>Prof. Dr. Ekhlass Saadallah Ahmed.<\/strong><\/p>\n<p><strong>The Thesis Addressed<\/strong><\/p>\n<p>This thesis aims to improve the numerical solutions of nonlinear ordinary and partial differential equations by developing hybrid methods combining wavelet analysis and Accelerated Adomian Analysis (ADM), using three wavelet families: Haar, CAS, and CAS-Haar.<\/p>\n<p>The thesis included the derivation of new general formulas and algorithms for solving ordinary and partial differential equations, as well as systems of differential equations, while demonstrating the theoretical convergence of the proposed methods. Adomian polynomials were also employed to handle nonlinear terms, transforming complex problems into simpler and more efficient algebraic systems.<\/p>\n<p>Finally, a new hybrid method using Accelerated Adomian Analysis (AADM) was developed. The results showed that this method achieved higher accuracy and better computational efficiency compared to the traditional hybrid method, with a significant reduction in absolute error and mean squared error (MSE).<\/p>\n<p>Finally, the conclusions were presented based on theoretical analysis and numerical comparisons, along with a set of recommendations for expanding these methods and applying them to nonlinear systems and more complex medical models.<\/p>\n<p><strong>The Discussion Committee Consisted of<\/strong><\/p>\n<ul>\n<li><strong>Prof. Dr. Saad Fawzi Jasim \u2014 Chair <\/strong><\/li>\n<li><strong>Prof. Dr. Abdulghafor M. Al-Rozbayani \u2014 Member<\/strong><\/li>\n<li><strong>Asst. Prof. Dr. Ahmed Farooq Qasim\u2014 Member<\/strong><\/li>\n<li><strong>Asst. Prof. Dr. Qasim Abbas Hussein \u2014 Member<\/strong><\/li>\n<li><strong>Asst. Prof. Dr. Ahmed Entesar Githeeth\u2014 Member<\/strong><\/li>\n<li><strong>Prof. Dr.<\/strong> <strong>Ekhlass Saadallah Ahmed \u2014 Member and Supervisor<\/strong><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Department of Mathematics Discussion of the doctoral thesis at the College of Computer Science and Mathematics, Department of Mathematics, entitled: \u201cImproving Wavelet Methods for Approximate Solutions of Nonlinear Partial Differential Equations\u201d supervised by Prof. Dr. Ekhlass Saadallah Ahmed. The Thesis Addressed This thesis aims to improve the numerical solutions of nonlinear ordinary and partial differential equations by developing hybrid methods combining wavelet analysis and Accelerated Adomian Analysis (ADM), using three wavelet families: Haar, CAS, and CAS-Haar. The thesis included the derivation of new general formulas and algorithms for solving ordinary and partial differential equations, as well as systems of differential equations, <a href=\"https:\/\/uomosul.edu.iq\/en\/computerscience\/2026\/08\/13\/1-703\/\"> [Read More]<\/a><\/p>\n","protected":false},"author":24,"featured_media":43236,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-43235","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-viva"],"_links":{"self":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/43235","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/users\/24"}],"replies":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/comments?post=43235"}],"version-history":[{"count":1,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/43235\/revisions"}],"predecessor-version":[{"id":43237,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/43235\/revisions\/43237"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media\/43236"}],"wp:attachment":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media?parent=43235"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/categories?post=43235"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/tags?post=43235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}