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


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Çakır M., Gunes B.

MATHEMATICS, vol.10, no.19, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Review
  • Volume: 10 Issue: 19
  • Publication Date: 2022
  • Doi Number: 10.3390/math10193560
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: error analysis, finite difference method, Fredholm integro-differential equation, singular perturbation, Volterra integro-differential equation, uniform convergence, CONVERGENCE ANALYSIS, NUMERICAL-METHOD, SYSTEM
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper presents a epsilon-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.