Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition

Durmaz M. E., Amiraliyev G. M., KUDU M.

Turkish Journal of Mathematics, vol.46, no.1, pp.207-224, 2022 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.3906/mat-2109-11
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.207-224
  • Keywords: Fredholm integro differential equation, singular perturbation, finite difference methods, Shishkin mesh, uniform convergence
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

© TÜBİTAKIn this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained.