Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations

Çakır M., Gunes B.

GEORGIAN MATHEMATICAL JOURNAL, vol.29, pp.193-203, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29
  • Publication Date: 2022
  • Doi Number: 10.1515/gmj-2021-2130
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.193-203
  • Keywords: Difference scheme, error estimate, Fredholm integro-differential equation, singular perturbation, uniform mesh, Volterra integro-differential equation, DECOMPOSITION METHOD, NUMERICAL-SOLUTION, APPROXIMATE, SYSTEM
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this study, singularly perturbed mixed integro-differential equations (SPMIDEs) are taken into account. First, the asymptotic behavior of the solution is investigated. Then, by using interpolating quadrature rules and an exponential basis function, the finite difference scheme is constructed on a uniform mesh. The stability and convergence of the proposed scheme are analyzed in the discrete maximum norm. Some numerical examples are solved, and numerical outcomes are obtained.