Boundary Value Problems
Volume 2010 (2010), Article ID 471793, 17 pages
doi:10.1155/2010/471793
Research Article

A Note on the Solution of the Von Kármán Equations Using Series and Chebyshev Spectral Methods

Zodwa G. Makukula,1 Precious Sibanda,1 and Sandile Sydney Motsa2

1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01 Scottsville, Pietermaritzburg 3209, South Africa
2Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni M201, Swaziland

Received 23 March 2010; Revised 2 August 2010; Accepted 2 October 2010

Academic Editor: Sandro Salsa

Copyright © 2010 Zodwa G. Makukula et al. 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

The classical von Kármán equations governing the boundary layer flow induced by a rotating disk are solved using the spectral homotopy analysis method and a novel successive linearisation method. The methods combine nonperturbation techniques with the Chebyshev spectral collocation method, and this study seeks to show the accuracy and reliability of the two methods in finding solutions of nonlinear systems of equations. The rapid convergence of the methods is determined by comparing the current results with numerical results and previous results in the literature.