A second-order difference scheme for the singularly perturbed Sobolev problems with third type boundary conditions on Bakhvalov mesh

Gunes B., Duru H.

Journal of Difference Equations and Applications, cilt.28, sa.3, ss.385-405, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/10236198.2022.2043289
  • Dergi Adı: Journal of Difference Equations and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.385-405
  • Anahtar Kelimeler: Bakhvalov mesh, error bounds, finite difference method, singular perturbation, Sobolev problem, PSEUDO-PARABOLIC EQUATIONS, CONVERGENCE ANALYSIS, NUMERICAL-METHOD, BLOW-UP, PARAMETER
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

© 2022 Informa UK Limited, trading as Taylor & Francis Group.We consider a singularly perturbed initial-third boundary value Sobolev problems. Firstly, the asymptotic behaviour of the exact solution is analysed. Then, a second-order finite difference scheme is constructed on the special non-uniform mesh. By using energy estimate, the stability and convergence of the proposed scheme are investigated in the discrete maximum norm. Finally, three numerical examples are solved to validate the theory.