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

This paper presents a <i>ε</i>-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...

Full description

Bibliographic Details
Published in:Mathematics
Main Authors: Musa Cakir, Baransel Gunes
Format: Article
Language:English
Published: MDPI AG 2022-09-01
Subjects:
error analysis
finite difference method
Fredholm integro-differential equation
singular perturbation
Volterra integro-differential equation
uniform convergence
Online Access:https://www.mdpi.com/2227-7390/10/19/3560
Description
Summary:This paper presents a <i>ε</i>-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.
ISSN:2227-7390

Similar Items