Numerical solution of singularly perturbed Fredholm integro-differential equations by homogeneous second order difference method

Durmaz M. E., Çakır M., AMİRALİ İ., AMİRALİ G.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.412, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 412
  • Publication Date: 2022
  • Doi Number: 10.1016/j.cam.2022.114327
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Fredholm integro-differential equation, Singular perturbation, Finite difference methods, Shishkin mesh, Uniform convergence, CONVERGENCE ANALYSIS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This work presents a computational approximate to solve singularly perturbed Fredholm integro-differential equation with the reduced second type Fredholm equation. This problem is discretized by a finite difference approximate, which generates second-order uniformly convergent numerical approximations to the solution. Parameter-uniform approximations are generated using Shishkin type meshes. The performance of the numerical scheme is tested which supports the effectiveness of the technique. (c) 2022 Elsevier B.V. All rights reserved.