A Second Order Fitted Numerical Method for a Singularly Perturbed Problem with an Integral Boundary Condition

Gurbuz B., Çakır M., Gunes B.

Mediterranean Journal of Mathematics, cilt.22, sa.7, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 7
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00009-025-02925-z
  • Dergi Adı: Mediterranean Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Finite difference scheme, Shishkin-type mesh, singular perturbation, uniform convergence
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This study provides the new discretization for the singularly perturbed problems with an integral boundary condition. Firstly, some properties of the continuous problem are given. Next, using the interpolating quadrature formulas (Amiraliyev and Mamedov in Turk J Math 19(3):207–222, 1995) and linear basis functions, the second-order difference scheme is generated on Shishkin-type mesh. The convergence and error approximations of the proposed scheme are analyzed. Two numerical examples are included to support the theoretical results.