Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method

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Abstract

The purpose of this study is to introduce a modification of the homotopy perturbation method using Laplace transform and Padé approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations. Two test examples are given; the coupled nonlinear system of Burger equations and the coupled nonlinear system in one dimensional thermoelasticity. The results obtained ensure that this modification is capable of solving a large number of nonlinear differential equations that have wide application in physics and engineering.

Keywords

Homotopy perturbation method
Padé approximation
Laplace transform
Coupled nonlinear Burger equations and 1-D thermo-elasticity

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