An Innovative Technique for Solving Singularly Perturbed Problems with Integral Boundary Conditions on the Non-Uniform Mesh

Temel Z., Çakır M.

Konuralp Journal of Mathematics, cilt.13, sa.1, ss.50-59, 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 1
  • Basım Tarihi: 2025
  • Dergi Adı: Konuralp Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.50-59
  • Anahtar Kelimeler: Integral Boundary, Linear Singularly Perturbed Problem, Non-Uniform Mesh, Numerical Method
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

We investigate an innovative numerical method for solving linear singularly perturbed problems with integral boundary conditions. Firstly, proving a uniformly convergent numerical method for solving the singularly perturbed problem is the main goal of this problem. Secondly, a piecewise equidistant mesh is used to generate the finite difference scheme. Next, the difference technique’s stability and convergence analysis are covered. Lastly, two test instances’ numerical results are shown.