A UNIFORM DISCRETIZATION FOR SOLVING SINGULARLY ERTURBED CONVECTION-DIFFUSION BOUNDARY VALUE PROBLEMS

Gunes B., Demirbas M.

Memoirs on Differential Equations and Mathematical Physics, vol.86, pp.69-84, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 86
  • Publication Date: 2022
  • Journal Name: Memoirs on Differential Equations and Mathematical Physics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.69-84
  • Keywords: Bakhvalov mesh, Boundary value problem, Convection-diffusion equation, Difference scheme, Error estimate, Shishkin mesh, Singular perturbation
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

© 2022, A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.In this paper, a discrete scheme is presented for solving singularly perturbed convection-diffusion equations. The stability and convergence of the proposed scheme are analyzed in the discrete maximum norm. Error estimates are carried out for both Bakhvalov (B-mesh) and Shishkin-type (S-mesh) meshes. Three numerical examples are solved to authenticate the theoretical findings.