A Fitted Operator Finite Difference Approximation for Singularly Perturbed Volterra–Fredholm Integro-Differential Equations

Musa Cakir () and Baransel Gunes
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Musa Cakir: Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Van 65080, Turkey
Baransel Gunes: Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Van 65080, Turkey

Mathematics, 2022, vol. 10, issue 19, 1-19

Abstract: This paper presents a ε -uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, and the finite difference scheme is established on a non-uniform mesh by using interpolating quadrature rules and the linear basis functions. An error analysis is successfully carried out on the Boglaev–Bakhvalov-type mesh. Some numerical experiments are included to authenticate the theoretical findings. In this regard, the main advantage of the suggested method is to yield stable results on layer-adapted meshes.

Keywords: error analysis; finite difference method; Fredholm integro-differential equation; singular perturbation; Volterra integro-differential equation; uniform convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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