Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Note on the Solution of the Von ´ ´ Karman Equations Using Series and Chebyshev Spectral Methods | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 471793 17 pages doi 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 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 Correspondence should be addressed to Precious Sibanda sibandap@ 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. The classical von Karman 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. 1. Introduction Most natural phenomena can be described by nonlinear equations that in general are not easy to solve in closed form. The search for computationally efficient robust and easy to use numerical and analytical techniques for solving nonlinear equations is therefore of great interest to researchers in engineering and science. The study of the steady laminar and axially symmetric viscous flow induced by an infinite disk rotating steadily with constant angular velocity was .
