Department of Mathematics Discussion of the doctoral thesis at the College of Computer Science and Mathematics, Department of Mathematics, entitled: “Improving Wavelet Methods for Approximate Solutions of Nonlinear Partial Differential Equations” 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, [Read More]