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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 564942, 10 pages
http://dx.doi.org/10.1155/2014/564942
Research Article

A Spectral Relaxation Approach for Unsteady Boundary-Layer Flow and Heat Transfer of a Nanofluid over a Permeable Stretching/Shrinking Sheet

1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa
2University of Swaziland, Private Bag 4, Kwaluseni, Swaziland

Received 20 March 2014; Accepted 10 April 2014; Published 28 April 2014

Academic Editor: Raseelo Joel Moitsheki

Copyright © 2014 S. S. Motsa 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

This paper introduces two novel numerical algorithms for the efficient solution of coupled systems of nonlinear boundary value problems. The methods are benchmarked against existing methods by finding dual solutions of the highly nonlinear system of equations that model the flow of a viscoelastic liquid of Oldroyd-B type in a channel of infinite extent. The methods discussed here are the spectral relaxation method and spectral quasi-linearisation method. To verify the accuracy and efficiency of the proposed methods a comparative evaluation of the performance of the methods against established numerical techniques is given.