A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh

Year 2022, Volume: 51 Issue: 3, 787 - 799, 01.06.2022

Musa Çakır , Baransel Güneş

https://doi.org/10.15672/hujms.950075

Cited By: 8

Abstract

In this research, the finite difference method is used to solve the initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit difference rules and composite numerical quadrature rules, the difference scheme is established on a Shishkin mesh. The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.

Keywords

difference scheme, error estimate, Fredholm integro-differential equation, singular perturbation, Shishkin mesh, Volterra integro-differential equation

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