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, vol.22, no.7, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 7
  • Publication Date: 2025
  • Doi Number: 10.1007/s00009-025-02925-z
  • Journal Name: Mediterranean Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Finite difference scheme, Shishkin-type mesh, singular perturbation, uniform convergence
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

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.