Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 41–57
Abstract
We obtain improved derivative estimates for the solution of the semilinear singularly perturbed reaction-diffusion problem in one dimension. This enables us to modify the transition points between the fine and coarse parts of the Shishkin discretization mesh. We prove that the numerical solution, obtained by using the central finite-difference scheme on the modified mesh, retains the same order of convergence uniform in the perturbation parameter as on the standard Shishkin mesh. However, the modified mesh may be denser in the layers than the standard one, and, when this is the case, numerical results show an improvement in the accuracy of the computed solution.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-425
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 41–57
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: singularly perturbed boundary-value problem reaction-diffusion Shishkin mesh finite differences and uniform convergence.