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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 941096, 10 pages
http://dx.doi.org/10.1155/2013/941096
Research Article

Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow 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 1 October 2013; Accepted 2 December 2013

Academic Editor: Waqar Khan

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 investigate the applicability of the compact finite difference relaxation method (CFDRM) in solving unsteady boundary layer flow problems modelled by nonlinear partial differential equations. The CFDRM utilizes the Gauss-Seidel approach of decoupling algebraic equations to linearize the governing equations and solve the resulting system of ordinary differential equations using compact finite difference schemes. The CFDRM has only been used to solve ordinary differential equations modelling boundary layer problems. This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. The CFDRM is validated on two examples and the results are compared to results of the Keller-box method.