A Note on the Solution of the Von Kármán Equations Using Series and Chebyshev Spectral Methods
1 School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01 Scottsville, Pietermaritzburg 3209, South Africa
2 Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni M201, Swaziland
Boundary Value Problems 2010, 2010:471793 doi:10.1155/2010/471793Published: 4 October 2010
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.