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Mathematical Problems in Engineering
Volume 2013, Article ID 746489, 15 pages
http://dx.doi.org/10.1155/2013/746489
Research Article

On the Comparison between Compact Finite Difference and Pseudospectral Approaches for Solving Similarity Boundary Layer Problems

1Department of Mathematics, University of Johannesburg, P.O. Box 17011, Doornfontein 2028, South Africa
2School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, Scottsville 3209, South Africa

Received 22 March 2013; Revised 15 July 2013; Accepted 26 July 2013

Academic Editor: Tirivanhu Chinyoka

Copyright © 2013 P. G. Dlamini 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

We introduce two methods based on higher order compact finite differences for solving boundary layer problems. The methods called compact finite difference relaxation method (CFD-RM) and compact finite difference quasilinearization method (CFD-QLM) are an alternative form of the spectral relaxation method (SRM) and spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral-based methods which have been successfully used to solve boundary layer problems. The main objective of this paper is to give a comparison of the compact finite difference approach against the pseudo-spectral approach in solving similarity boundary layer problems. In particular, we seek to identify the most accurate and computationally efficient method for solving systems of boundary layer equations in fluid mechanics. The results of the two approaches are comparable in terms of accuracy for small systems of equations. For larger systems of equations, the proposed compact finite difference approaches are more accurate than the spectral-method-based approaches.