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Mathematical Problems in Engineering
Volume 2013, Article ID 635392, 7 pages
http://dx.doi.org/10.1155/2013/635392
Research Article

On the Successive Linearisation Approach to the Flow of Reactive Third-Grade Liquid in a Channel with Isothermal Walls

1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa
2Institute for Advanced Research in Mathematical Modelling and Computations, Cape Peninsula University of Technology, P.O. Box 1906, Bellville 7535, South Africa
3Department of Mathematics & Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 27 March 2013; Accepted 30 April 2013

Academic Editor: Anuar Ishak

Copyright © 2013 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

The nonlinear differential equations modeling flow of a reactive third-grade liquid between two parallel isothermal plates is investigated using a novel hybrid of numerical-analytical scheme known as the successive linearization method (SLM). Numerical and graphical results obtained show excellence in agreement with the earlier results reported in the literature. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver bvp4c demonstrates that the new SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.