Table of Contents
Journal of Computational Methods in Physics
Volume 2014, Article ID 512702, 7 pages
http://dx.doi.org/10.1155/2014/512702
Research Article

Spectral-Homotopy Perturbation Method for Solving Governing MHD Jeffery-Hamel Problem

Faculty of Technology of Mathematical Sciences and Statistics, Al-Neelain University, Algamhoria Street, P.O. Box 12702, Khartoum, Sudan

Received 20 February 2014; Revised 3 July 2014; Accepted 7 July 2014; Published 14 July 2014

Academic Editor: Xavier Ferrieres

Copyright © 2014 Ahmed A. Khidir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a new modification of the homotopy perturbation method (HPM) for solving nonlinear boundary value problems. The technique is based on the standard homotopy perturbation method and blending of the Chebyshev pseudospectral methods. The implementation of the new approach is demonstrated by solving the MHD Jeffery-Hamel flow and the effect of MHD on the flow has been discussed. Comparisons are made between the proposed technique, the previous studies, the standard homotopy perturbation method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the presented approach. The results demonstrate that the new modification is more efficient and converges faster than the standard homotopy perturbation method at small orders. The MATLAB software has been used to solve all the equations in this study.