A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition

Baransel Gunes; Musa Cakir

doi:10.3842/umzh.v76i1.7331

Baransel Gunes Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Turkey
Musa Cakir Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Turkey

DOI: https://doi.org/10.3842/umzh.v76i1.7331

Keywords: Finite difference method, integral boundary condition, integro-differential equation, singular perturbation, uniform convergence

Abstract

UDC 517.9

We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra–Fredholm integro-differential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain the approximate solution of the presented problem. It is proven that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.

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