Finite Difference Method for Singularly Perturbed Non-local Boundary Value Problems on Bakhvalov-Shishkin Mesh

Abstract

This study aims to achieve a precise computational solution for a linear singularly perturbed problem with a non-local boundary condition using discritization of the Bakhvalov-Shishkin mesh. A conventional finite difference scheme was developed to approximate the problem, while the composite Simpson’s 1/3 rule was used to approximate the boundary portion of the integral. By analyzing the ε-perturbation parameter, achieved a fitted mesh finite difference method and it was determined that the first-order uniform convergence adhered to the dis crete maximum norm. To showcase the effectiveness and accuracy of the proposed method, a numerical experiment was conducted and the results were validated using appropriate tables and figures.