A NOVEL NUMERICAL TECHNIQUE FOR SOLVING SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS WITH MIXED BOUNDARY CONDITIONS

Temel Z., Çakır M.

Journal of Mathematical Analysis, cilt.16, sa.1, ss.20-31, 2025 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.54379/jma-2025-1-2
  • Dergi Adı: Journal of Mathematical Analysis
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.20-31
  • Anahtar Kelimeler: Boundary layer, Numerical solution, Singularly perturbed problem, Uniform convergence
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

We investigate an innovative numerical technique for a singularly perturbed problem that has an integral boundary condition. To solve the problem, first the boundary values and their derivatives are determined. And then, the difference scheme is constructed on the Shishkin mesh. And also, we analyze the uniform convergence and stability of the scheme with a perturbation parameter. Next, the numerical technique’s convergence and stability are discussed and tested. Numerical results verify the theoretical conclusions as well.