A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh


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Çakır M., Gunes B.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.3, pp.787-799, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.15672/hujms.950075
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.787-799
  • Keywords: Keywords, difference scheme, error estimate, Fredholm integro-differential equation, singular perturbation, Shishkin mesh, Volterra integro-differential equation, COLLOCATION METHOD, DECOMPOSITION METHOD
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this research, the finite difference method is used to solve the initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit difference rules and composite numerical quadrature rules, the difference scheme is established on a Shishkin mesh. The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.