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Volume 7, Issue 3
Second Order Uniform Approximations for the Solution of Time Dependent Singularly Perturbed Reaction-Diffusion Systems

C. Clavero, J. L. Gracia & F. Lisbona

Int. J. Numer. Anal. Mod., 7 (2010), pp. 428-443.

Published online: 2010-07

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  • Abstract

In this work we consider a parabolic system of two linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms. To obtain an efficient approximation of the exact solution we propose a numerical method combining the Crank-Nicolson method used in conjunction with the central finite difference scheme defined on a piecewise uniform Shishkin mesh. The method gives uniform numerical approximations of second order in time and almost second order in space. Some numerical experiments are given to support the theoretical results.

  • Keywords

Reaction-diffusion problems, uniform convergence, coupled system, Shishkin mesh, second order.

  • AMS Subject Headings

65M06, 65N06, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-428, author = {C. Clavero, J. L. Gracia and F. Lisbona}, title = {Second Order Uniform Approximations for the Solution of Time Dependent Singularly Perturbed Reaction-Diffusion Systems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {428--443}, abstract = {

In this work we consider a parabolic system of two linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms. To obtain an efficient approximation of the exact solution we propose a numerical method combining the Crank-Nicolson method used in conjunction with the central finite difference scheme defined on a piecewise uniform Shishkin mesh. The method gives uniform numerical approximations of second order in time and almost second order in space. Some numerical experiments are given to support the theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/729.html} }
TY - JOUR T1 - Second Order Uniform Approximations for the Solution of Time Dependent Singularly Perturbed Reaction-Diffusion Systems AU - C. Clavero, J. L. Gracia & F. Lisbona JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 428 EP - 443 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/729.html KW - Reaction-diffusion problems, uniform convergence, coupled system, Shishkin mesh, second order. AB -

In this work we consider a parabolic system of two linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms. To obtain an efficient approximation of the exact solution we propose a numerical method combining the Crank-Nicolson method used in conjunction with the central finite difference scheme defined on a piecewise uniform Shishkin mesh. The method gives uniform numerical approximations of second order in time and almost second order in space. Some numerical experiments are given to support the theoretical results.

C. Clavero, J. L. Gracia and F. Lisbona. (2010). Second Order Uniform Approximations for the Solution of Time Dependent Singularly Perturbed Reaction-Diffusion Systems. International Journal of Numerical Analysis and Modeling. 7 (3). 428-443. doi:
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