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A Uniformly Convergent Numerical Method for Singularly Perturbed Semilinear Integro-Differential Equations With Two Integral Boundary Conditions

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Date

2023

Journal Title

Journal ISSN

Volume Title

Publisher

Pleiades Publishing inc

Abstract

This paper purposes to present a new discrete scheme for the singularly perturbed semilinear Volterra-Fredholm integro-differential equation including two integral boundary conditions. Initially, some analytical properties of the solution are given. Then, using the composite numerical integration formulas and implicit difference rules, the finite difference scheme is established on a uniform mesh. Error approximations for the approximate solution and stability bounds are investigated in the discrete maximum norm. Finally, a numerical example is solved to show epsilon-uniform convergence of the suggested difference scheme.

Description

Keywords

Discrete Scheme, Error Bounds, Integral Boundary Condition, Integro-Differential Equation, Singular Perturbation

Turkish CoHE Thesis Center URL

WoS Q

Q4

Scopus Q

Q3

Source

Volume

63

Issue

12

Start Page

2513

End Page

2527