A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition

Gunes B., Çakır M.

Ukrainian Mathematical Journal, cilt.76, sa.1, ss.122-140, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 76 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s11253-024-02312-z
  • Dergi Adı: Ukrainian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.122-140
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.