Journal of Applied Mathematics
Volume 2013 (2013), Article ID 879195, 9 pages
Research Article

On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method

School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa

Received 22 January 2013; Revised 22 March 2013; Accepted 5 April 2013

Academic Editor: Saeid Abbasbandy

Copyright © 2013 Sandile S. Motsa and Precious Sibanda. 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.


We propose a sequence of highly accurate higher order convergent iterative schemes by embedding the quasilinearization algorithm within a spectral collocation method. The iterative schemes are simple to use and significantly reduce the time and number of iterations required to find solutions of highly nonlinear boundary value problems to any arbitrary level of accuracy. The accuracy and convergence properties of the proposed algorithms are tested numerically by solving three Falkner-Skan type boundary layer flow problems and comparing the results to the most accurate results currently available in the literature. We show, for instance, that precision of up to 29 significant figures can be attained with no more than 5 iterations of each algorithm.