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

Amin A. Z. M. A., Abdelkawy M., Soluma E., Babatin M.

International Journal of Modern Physics C, vol.35, no.7, 2024 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 7
  • Publication Date: 2024
  • Doi Number: 10.1142/s0129183124500888
  • 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: Riemann-Liouville fractional of variable order, shifted Legendre and Chebyshev polynomials, Variable-order fractional convection-diffusion equations
  • Istanbul Gelisim University Affiliated: No

Abstract

The study focuses on the numerical solutions of two-dimensional variable-order fractional convection-diffusion equations, which combine the principles of diffusion and convection to describe the movement of particles, energy, other physical quantities within a system. The numerical solution is obtained using shifted Legendre Gauss-Lobatto and shifted Chebyshev Gauss-Radau collocation techniques. The convection-diffusion equation is transformed into a system of algebraic equations utilizing shifted Chebyshev Gauss-Radau and shifted Legendre Gauss-Lobatto nodes. Additionally, numerical test examples are presented to demonstrate the method's efficacy to handle nonsmooth solutions to the given problems.