Volume 10, Issue 3
An Almost Fourth Order Parameter-Robust Numerical Method for a Linear System of ($M\geq2$) Coupled Singularly Perturbed Reaction-Diffusion Problems

S. C. S. Rao & M. Kumar

Int. J. Numer. Anal. Mod., 10 (2013), pp. 603-621.

Published online: 2013-10

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  • Abstract

We present a high order parameter-robust finite difference method for a linear system of ($M\geq2$) coupled singularly perturbed reaction-diffusion two point boundary value problems. The problem is discretized using a suitable combination of the fourth order compact difference scheme and the central difference scheme on a generalized Shishkin mesh. A high order decomposition of the exact solution into its regular and singular parts is constructed. The error analysis is given and the method is proved to have almost fourth order parameter robust convergence, in the maximum norm. Numerical experiments are conducted to demonstrate the theoretical results.

  • Keywords

Parameter-robust convergence, System of coupled reaction-diffusion problem, Generalized-Shishkin mesh, Fourth order compact difference scheme, Central difference scheme.

  • AMS Subject Headings

65L10, 65L11

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-603, author = {Rao , S. C. S. and Kumar , M.}, title = {An Almost Fourth Order Parameter-Robust Numerical Method for a Linear System of ($M\geq2$) Coupled Singularly Perturbed Reaction-Diffusion Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {3}, pages = {603--621}, abstract = {

We present a high order parameter-robust finite difference method for a linear system of ($M\geq2$) coupled singularly perturbed reaction-diffusion two point boundary value problems. The problem is discretized using a suitable combination of the fourth order compact difference scheme and the central difference scheme on a generalized Shishkin mesh. A high order decomposition of the exact solution into its regular and singular parts is constructed. The error analysis is given and the method is proved to have almost fourth order parameter robust convergence, in the maximum norm. Numerical experiments are conducted to demonstrate the theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/585.html} }
TY - JOUR T1 - An Almost Fourth Order Parameter-Robust Numerical Method for a Linear System of ($M\geq2$) Coupled Singularly Perturbed Reaction-Diffusion Problems AU - Rao , S. C. S. AU - Kumar , M. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 603 EP - 621 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/585.html KW - Parameter-robust convergence, System of coupled reaction-diffusion problem, Generalized-Shishkin mesh, Fourth order compact difference scheme, Central difference scheme. AB -

We present a high order parameter-robust finite difference method for a linear system of ($M\geq2$) coupled singularly perturbed reaction-diffusion two point boundary value problems. The problem is discretized using a suitable combination of the fourth order compact difference scheme and the central difference scheme on a generalized Shishkin mesh. A high order decomposition of the exact solution into its regular and singular parts is constructed. The error analysis is given and the method is proved to have almost fourth order parameter robust convergence, in the maximum norm. Numerical experiments are conducted to demonstrate the theoretical results.

S. C. S. Rao & M. Kumar. (1970). An Almost Fourth Order Parameter-Robust Numerical Method for a Linear System of ($M\geq2$) Coupled Singularly Perturbed Reaction-Diffusion Problems. International Journal of Numerical Analysis and Modeling. 10 (3). 603-621. doi:
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