### An Effective Numerical Method for Singularly Perturbed Nonlocal Boundary Value Problem on Bakhvalov Mesh

Derya Arslan

#### Abstract

The present study focuses on obtaining an absolutely accurate computational solution of a linear singularly perturbed problem with integral boundary condition on Bakhvalov mesh. A finite difference scheme was constructed and the approximation of the presented problem was obtained. Based on the $$\varepsilon$$-perturbation parameter, it was established that the first-order uniform convergence was within the discrete maximum norm. A numerical experiment was performed in order to demonstrate the effectiveness and accuracy of the presented method. The results were confirmed through the relevant table and figures.

#### Keywords

Singular perturbation; Finite difference scheme; Bakhvalov mesh; Uniformly convergence; Integral boundary condition

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DOI: http://dx.doi.org/10.26713%2Fjims.v11i3-4.1088

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