Journal of Mathematics and Statistics

A New Approach to Solve Nonlinear Partial Differential Equations

Abdoul R. Ghotbi, M. A. Mohammadzade, A. Avaei and M. Keyvanipoor

DOI : 10.3844/jmssp.2007.201.206

Journal of Mathematics and Statistics

Volume 3, Issue 4

Pages 201-206

Abstract

Nonlinear phenomena play a crucial role in applied mathematics and physics. Explicit solutions to the nonlinear equations are of fundamental importance. Various methods for obtaining explicit solution to nonlinear evolution equations have been proposed. In this letter homotopy perturbation method (HPM) is employed for solving one-dimensional non-homogeneous parabolic partial differential equation with a variable coefficient and a system of nonlinear partial differential equations. The final results obtained by means of HPM, were compared with those results obtained from the exact solution and the Adomian Decomposition Method (ADM). The comparison shows a precise agreement between the results, and introduces this new method as an applicable one which it needs less computations and is much easier and more convenient than others, so it can be widely used in engineering too.

Copyright

© 2007 Abdoul R. Ghotbi, M. A. Mohammadzade, A. Avaei and M. Keyvanipoor. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.