A Uniformly Convergent Numerical Study on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem

Authors

  • Derya Arslan Department of Mathematics, Faculty of Art and Science, Bitlis Eren University, 13200, Bitlis

DOI:

https://doi.org/10.26713/cma.v11i1.1349

Keywords:

Singular perturbation, Finite difference scheme, Bakhvalov-Shishkin mesh, Uniformly convergence, Multipoint boundary condition, Discrete maximum norm

Abstract

In this paper, singularly perturbed multipoint boundary value problem with a right boundary layer is considered. This problem is discretized using finite difference method on Bakhvalov-Shishkin type mesh. We give uniform error estimate in a discrete maximum norm. The first-order of accuracy difference schemes for the approximate solutions of the problem are presented. The obtained numerical results demonstrate that the convergence rate of difference scheme is in accord with the theoretical analysis which means that the theoretical results are fairly sharp.

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Published

31-03-2020
CITATION

How to Cite

Arslan, D. (2020). A Uniformly Convergent Numerical Study on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem. Communications in Mathematics and Applications, 11(1), 161–171. https://doi.org/10.26713/cma.v11i1.1349

Issue

Vol. 11 No. 1 (2020)

Section

Research Article

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