Modified Algorithm to Compute Adomian's Polynomial for Solving Non-Linear Systems of Partial Differential Equations

Abstract

In this paper, we modified the method of computing Adomian's polynomial to find the numerical solution for non-linear systems of partial differential equations (PDEs) with less number of components, more accuracy and faster convergence when compared with the standard Adomian decomposition method (ADM). The partial differential equations (PDEs) have so many essential applications of science and engineering such as fluid mechanic, thermodynamic, heat transfer, physics, chemistry , micro electro mechanic system, etc. Most of these equations are nonlinear PDEs which are employed in modeling many physical and scientific phenomena such as thermal engineering, acoustic, electromagnetism, control, robotics, viscosity, diffusion, edge detection, turbulence, signal processing and many other processes. It is difficult to handle nonlinear part of these equations, although most of the scientists applied numerical methods to find the solution of these equations that based on linearization, perturbation, discretization.