An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation

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Durmaz M. E., YAPMAN Ö., KUDU M., Amiraliyev G. M.

Hacettepe Journal of Mathematics and Statistics, cilt.52, sa.2, ss.326-339, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.15672/hujms.1050505
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.326-339
  • Anahtar Kelimeler: finite difference methods, integro-differential equation, Shishkin mesh, singular perturbation, uniform convergence
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

The scope of this study is to establish an effective approximation method for linear first order singularly perturbed Volterra-Fredholm integro-differential equations. The finite difference scheme is constructed on Shishkin mesh by using appropriate interpolating quadrature rules and exponential basis function. The recommended method is second order convergent in the discrete maximum norm. Numerical results illustrating the preciseness and computationally attractiveness of the proposed method are presented.