Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type
Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 3 : pp. 265–287
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.y12030
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 3 : pp. 265–287
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Singularly perturbed problems third order ordinary differential equations boundary value technique asymptotic expansion approximation shooting method finite difference scheme parallel computation.
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Numerical solution of a fourth‐order singularly perturbed boundary value problem with discontinuities via Haar wavelets
Podila, Pramod Chakravarthy
Sundrani, Vishwas
Ramos, Higinio
Mathematical Methods in the Applied Sciences, Vol. 45 (2022), Iss. 17 P.10904
https://doi.org/10.1002/mma.8424 [Citations: 3]