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, cilt.34, sa.3, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s0129183123500419
  • 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: Chebyshev polynomials, fractional calculus, Riemann–Liouville fractional of variable order, shifted Legendre, spectral collocation method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

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.