Open Access Research

An improved spectral homotopy analysis method for solving boundary layer problems

Sandile Sydney Motsa1, Gerald T Marewo1, Precious Sibanda2 and Stanford Shateyi3*

Author Affiliations

1 Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni, Swaziland

2 School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa

3 Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

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Boundary Value Problems 2011, 2011:3  doi:10.1186/1687-2770-2011-3

Published: 22 June 2011

Abstract

This article presents an improved spectral-homotopy analysis method (ISHAM) for solving nonlinear differential equations. The implementation of this new technique is shown by solving the Falkner-Skan and magnetohydrodynamic boundary layer problems. The results obtained are compared to numerical solutions in the literature and MATLAB's bvp4c solver. The results show that the ISHAM converges faster and gives accurate results.

Keywords:
Falkner-Skan flow; MHD flow; improved spectral-homotopy analysis method