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, cilt.35, sa.7, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 7
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s0129183124500888
  • Dergi Adı: International Journal of Modern Physics C
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, zbMATH
  • Anahtar Kelimeler: Riemann-Liouville fractional of variable order, shifted Legendre and Chebyshev polynomials, Variable-order fractional convection-diffusion equations
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

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.