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

Authors : Muhammet Enes DURMAZ, Ömer YAPMAN, Mustafa KUDU, Gabil AMİRALİ

Pages : 326-339

Doi:10.15672/hujms.1050505

View : 23 | Download : 6

Publication Date : 2023-03-31

Article Type : Research Paper

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