Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method

Mohamed S M Bahgat

doi:10.24297/jam.v12i8.5075

Abstract

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components.

Highlights

The partial differential equations (PDEs) have so many essential applications of science and engineering such as wave propagation, shallow water waves, fluid mechanics, thermodynamic, chemistry and micro electro mechanic system, etc
Laplace Decomposition Method (LDM) is free of any small or large parameters and has advantages over other approximation techniques like perturbation, LDM requires no discretization and linearization, results obtained by LDM are more efficient and realistic
In order to verify numerically whether the proposed methodology leads to the accurate solutions, we evaluate Laplace Adomian Decomposition Method (LADM) using the approximation for some examples of non-linear systems of PDEs

Summary

INTRODUCTION

The partial differential equations (PDEs) have so many essential applications of science and engineering such as wave propagation, shallow water waves, fluid mechanics, thermodynamic, chemistry and micro electro mechanic system, etc. Debnath [1] applied the characteristics method and Logan [2] used the Rieman invariants method to handle systems of PDEs. Wazwaz [3] used the Adomian decomposition method (ADM) to handle the systems of PDEs. Laplace Decomposition Method (LDM) is free of any small or large parameters and has advantages over other approximation techniques like perturbation, LDM requires no discretization and linearization, results obtained by LDM are more efficient and realistic. Laplace Decomposition Method (LDM) is free of any small or large parameters and has advantages over other approximation techniques like perturbation, LDM requires no discretization and linearization, results obtained by LDM are more efficient and realistic This method has been used to obtain approximate solutions of a class of nonlinear ordinary and PDEs [4,5,6,7]. The numerical solutions become easier and higher accuracy than the standard Adomian Decomposition Method (ADM)

LADM for NONLINEAR COUPLED of PDEs

APPLICATIONS

CONCLUSION