A fully discrete scheme on piecewise-equidistant mesh for singularly perturbed delay integro-differential equations

Çakır M., Gunes B.

Quaestiones Mathematicae, vol.47, no.9, pp.1913-1933, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 9
  • Publication Date: 2024
  • Doi Number: 10.2989/16073606.2024.2343669
  • Journal Name: Quaestiones Mathematicae
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1913-1933
  • Keywords: Delay differential equation, difference scheme, integro-differential equation, singular perturbation, uniform convergence
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Abstract.: This paper chiefly takes into account the singularly perturbed delay Volterra-Fredholm integro-differential equations by numerically. In this context, firstly, priori estimates are given and a new discretization is constructed on piecewise-equidistant mesh by using interpolating quadrature rules [2] and composite integration formulas. Then, the convergence analysis and stability bounds of the presented method are discussed. Finally, numerical results are demonstrated with two test problems.