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

Izadi M., YÜZBAŞI Ş.

Mathematical Communications, cilt.27, sa.1, ss.47-62, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 1
  • Basım Tarihi: 2022
  • Dergi Adı: Mathematical Communications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.47-62
  • Anahtar Kelimeler: collocation points, convection-diffusion problem, special polynomials, Taylor expansion
  • Akdeniz Üniversitesi Adresli: Evet

Özet

© 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.