Volume 7, Issue 3
Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type

J. Christy Roja & A. Tamilselvan

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 265-287.

Published online: 2014-07

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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

Singularly perturbed problems, third order ordinary differential equations, boundary value technique, asymptotic expansion approximation, shooting method, finite difference scheme, parallel computation.

  • AMS Subject Headings

65L10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-265, author = {}, title = {Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {3}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.y12030}, url = {http://global-sci.org/intro/article_detail/nmtma/5875.html} }
TY - JOUR T1 - Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 265 EP - 287 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.y12030 UR - https://global-sci.org/intro/article_detail/nmtma/5875.html KW - Singularly perturbed problems, third order ordinary differential equations, boundary value technique, asymptotic expansion approximation, shooting method, finite difference scheme, parallel computation. AB -

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.

J. Christy Roja & A. Tamilselvan. (2020). Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type. Numerical Mathematics: Theory, Methods and Applications. 7 (3). 265-287. doi:10.4208/nmtma.2014.y12030
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