Enhanced Adomian Decomposition Method for Accurate Numerical Solutions of PDE Systems
Saleh Ali Alomari *
Department of Mathematics, Faculty of Education and Sciences, Albaydha University, Yemen.
Yahya Qaid Hasan
Department of Mathematics, Faculty of Applied Science, Thamar University, Yemen.
*Author to whom correspondence should be addressed.
Abstract
This research addresses critical challenges in numerical solutions, which are vital for various engineering and physical fields. The Modified Adomian Decomposition Method (MADM) is proposed as a novel approach for solving linear and nonlinear partial differential equations (PDEs). MADM builds upon the Adomian Decomposition Method (ADM) by incorporating a new integral operator that significantly improves convergence rates and accuracy.
Numerical examples demonstrate the effectiveness of MADM in handling complex nonlinear PDEs. Compared to traditional ADM, MADM consistently achieves more accurate and rapidly converging solutions. This enhancement is attributed to the novel integral operator, which addresses the limitations of ADM for intricate nonlinear problems.
The paper outlines the application of MADM, its solution procedure, and its effectiveness through numerical examples. Comparisons with standard ADM solutions and exact solutions validate MADM's accuracy and superiority. The results suggest that MADM is a promising tool for expanding the applicability of Adomian methods in the field of solving PDEs.
Keywords: Adomian decomposition method, system of PDEs, numerical methods, accuracy, convergence, approximate solutions