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

This paper presents a ε-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 interpolatin...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-09, Vol.10 (19), p.3560
Main Authors: Cakir, Musa, Gunes, Baransel
Format: Article
Language:English
Subjects:
Analysis
Approximation theory
Basis functions
Differential equations
Error analysis
Exact solutions
Finite difference method
Flow control
Fredholm integro-differential equation
Mathematical analysis
Methods
Operators (mathematics)
Pandemics
Perturbation (Mathematics)
Quadratures
singular perturbation
uniform convergence
Volterra integro-differential equation
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Summary:This paper presents a ε-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
2227-7390
DOI:10.3390/math10193560