An Innovative Technique for Solving Singularly Perturbed Problems with Integral Boundary Conditions on the Non-Uniform Mesh

Year 2025, Volume: 13 Issue: 1, 50 - 59, 30.04.2025

Zelal Temel , Musa Çakır

Abstract

We investigate an innovative numerical method for solving linear singularly perturbed problems with integral boundary conditions. Firstly, proving a uniformly convergent numerical method for solving the singularly perturbed problem is the main goal of this problem. Secondly, a piecewise equidistant mesh is used to generate the finite difference scheme. Next, the difference technique's stability and convergence analysis are covered. Lastly, two test instances' numerical results are shown.

Keywords

Linear Singularly Perturbed Problem, Non-Uniform Mesh, Numerical Method, Integral Boundary.

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