Method of Exact Difference Schemes for the Numerical Solution of Parameterized Singularly Perturbed Problem

YAPMAN Ö., KUDU M., Amiraliyev G. M.

Mediterranean Journal of Mathematics, cilt.20, sa.3, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00009-023-02360-y
  • Dergi Adı: Mediterranean Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Volterra integro-differential equation, singular perturbation, finite difference method, uniform convergence, parameterized problem
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

In this paper, we study a uniform finite difference method for the first-order singularly perturbed Volterra integro-differential problem depending on a parameter. We prove that the method is uniform second-order convergent except for a logarithmic factor in the discrete maximum norm. Numerical results are presented which are in agreement with the theoretical analysis.