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Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type

Published online by Cambridge University Press:  28 May 2015

J. Christy Roja  and
A. Tamilselvan
J. Christy Roja
Affiliation:
Department of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamilnadu, India
A. Tamilselvan*
Affiliation:
Department of Mathematics, Bharathidasan University, Tiruchirappalli-620 024, Tamilnadu, India
*
*Corresponding author.Email address:thamizh66@gmail.com
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Abstract

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of convection-diffusion type of third order Ordinary Differential Equations (ODEs) in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. In order to get a numerical solution for the derivative of the solution, the domain is divided into two regions namely inner region and outer region. The shooting method is applied to the inner region while standard finite difference scheme (FD) is applied for the outer region. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing.

Keywords

65L10Singularly perturbed problemsthird order ordinary differential equationsboundary value techniqueasymptotic expansion approximationshooting methodfinite difference schemeparallel computation
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 3 , August 2014 , pp. 265 - 287
Copyright
Copyright © Global Science Press Limited 2014

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