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, cilt.150, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 150
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.chaos.2021.111100
  • Dergi Adı: Chaos, Solitons and Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Anahtar Kelimeler: Volterra delay-integro-differential equation, Singular perturbation, Finite difference method, Uniform convergence, LINEAR MULTISTEP METHODS, INTEGRODIFFERENTIAL EQUATIONS, STABILITY ANALYSIS, BEHAVIOR
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

© 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.