A Robust Numerical Method For The Singularly Perturbed Integro-Differential Equations

Year 2025, Volume: 38 Issue: 1, 267 - 273, 01.03.2025

Derya Arslan , Ercan Celık

https://doi.org/10.35378/gujs.1498203

Abstract

In the present study, NIM is given to approximate the solution of SPFIDEs. As a first step, the FDM on a uniform mesh is used, followed by the TM for integrals. After these calculations, the difference equation is obtained in the form of a system of equations. This system of equations is solved with the TA. Finally, example applications are made, showing the accuracy and economics of the presented method.

Keywords

Singularly Perturbed Problem(SPP) , Fredholm Integro-Differential Equation(FIDE) , Numerical Integration Method(NIM) , Finite difference Method(FDM) , Thomas Algorithm(TA)

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