Convergence analysis of the homogeneous second order difference method for a singularly perturbed Volterra delay-integro-differential equation


YAPMAN Ö., AMİRALİ G.

Chaos, Solitons and Fractals, vol.150, 2021 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 150
  • Publication Date: 2021
  • Doi Number: 10.1016/j.chaos.2021.111100
  • Journal Name: Chaos, Solitons and Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Keywords: Volterra delay-integro-differential equation, Singular perturbation, Finite difference method, Uniform convergence, LINEAR MULTISTEP METHODS, INTEGRODIFFERENTIAL EQUATIONS, STABILITY ANALYSIS, BEHAVIOR
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

© 2021 Elsevier LtdA linear Volterra delay-integro-differential equation with a singular perturbation parameter ε is considered. The problem is discretized using exponentially fitted schemes on the Shishkin type meshes. It is proved that the numerical approximations generated by this method are O(N−2lnN) convergent in the discrete maximum norm, where N is the mesh parameter. Numerical results show a good agreement with the theoretical analysis.