A space-time spectral approximation for solving nonlinear variable-order fractional convection-diffusion equations with nonsmooth solutions

Amin A. Z. M. A., Abdelkawy M., Hashim I.

International Journal of Modern Physics C, vol.34, no.3, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1142/s0129183123500419
  • Journal Name: International Journal of Modern Physics C
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, zbMATH
  • Keywords: Chebyshev polynomials, fractional calculus, Riemann–Liouville fractional of variable order, shifted Legendre, spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

One of the problems in the numerical analysis of solutions is the nonlinear variable-order fractional convection-diffusion equations for nonsmooth solutions. We offer a numerical technique based on the shifted Legendre Gauss-Lobatto collocation and the shifted Chebyshev Gauss-Radau collocation to solve the problem. The technique with shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau nodes is applied to diminish nonlinear variable-order fractional convection-diffusion equations to an easily-solvable system of algebraic equations. Besides, we give numerical test examples to show that the approach can preserve the nonsmooth solution of the underlying problems.