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

Derya Arslan

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.


Keywords


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

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v11i1.1349

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