An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation

Muhammet Enes Durmaz; Ömer Yapman; Mustafa Kudu; Gabil Amirali

doi:10.15672/hujms.1050505

Research Article

An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation

Year 2023, Volume: 52 Issue: 2, 326 - 339, 31.03.2023

Muhammet Enes Durmaz , Ömer Yapman , Mustafa Kudu , Gabil Amirali

https://doi.org/10.15672/hujms.1050505

Cited By: 10

https://izlik.org/JA86CS88DN

Abstract

The scope of this study is to establish an effective approximation method for linear first order singularly perturbed Volterra-Fredholm integro-differential equations. The finite difference scheme is constructed on Shishkin mesh by using appropriate interpolating quadrature rules and exponential basis function. The recommended method is second order convergent in the discrete maximum norm. Numerical results illustrating the preciseness and computationally attractiveness of the proposed method are presented.

Keywords

finite difference methods , integro-differential equation , Shishkin mesh , singular perturbation , uniform convergence

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