A hybrid approximation scheme for 1-D singularly perturbed parabolic convection-diffusion problems

Izadi M., YÜZBAŞI Ş.

Mathematical Communications, vol.27, no.1, pp.47-62, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 1
  • Publication Date: 2022
  • Journal Name: Mathematical Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.47-62
  • Keywords: collocation points, convection-diffusion problem, special polynomials, Taylor expansion
  • Akdeniz University Affiliated: Yes

Abstract

© 2022 Department of Mathematics, University of Osijek.Our study is concerned with a hybrid spectral collocation approach to solving singularly perturbed 1-D parabolic convection-diffusion problems. In this approach, discretization in time is carried out with the help of Taylor series expansions before the spectral based on novel special polynomials is applied to the spatial operator in the time step. A detailed error analysis of the presented technique is conducted with regard to the space variable. The advantages of this attempt are presented through comparison of our results in the model problems obtained by this technique and other existing schemes.