A second-order numerical approximation of a singularly perturbed nonlinear Fredholm integro-differential equation

Durmaz M. E., Amirali I., Mohapatra J., Amiraliyev G. M.

Applied Numerical Mathematics, vol.191, pp.17-28, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 191
  • Publication Date: 2023
  • Doi Number: 10.1016/j.apnum.2023.05.008
  • Journal Name: Applied Numerical Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.17-28
  • Keywords: Finite difference methods, Integro-differential equation, Richardson extrapolation, Singular perturbation, Uniform convergence
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

We consider a singularly perturbed problem for a nonlinear first-order Fredholm integro-differential equation. Our aim is to build and analyze a numerical approach with uniform convergence in the ε-parameter. The numerical solution of problem is discretized utilizing interpolation quadrature formulas for the differential part and the composite rectangular rule for the integral part. Error estimations for the approximate solution are established. In support of the idea, numerical examples are provided.