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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 410620, 6 pages
http://dx.doi.org/10.1155/2014/410620
Research Article

Application of Successive Linearisation Method to Squeezing Flow with Bifurcation

1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa
2Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa
3Department of Mathematics & Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 28 September 2013; Accepted 16 December 2013; Published 2 January 2014

Academic Editor: R. N. Jana

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 employs the computational approach known as successive linearization method (SLM) to tackle a fourth order nonlinear differential equation modelling the transient flow of an incompressible viscous fluid between two parallel plates produced by a simple wall motion. Numerical and graphical results obtained show excellent agreement with the earlier results reported in the literature. We obtain solution branches as well as a turning point in the flow field accurately. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver, bvp4c, demonstrates that the SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.