Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

• Autor(a) principal: Bhrawy, A. H.
• Data de Publicação: 2015
• Outros Autores: Zaky, M.A., Machado, J. A. Tenreiro
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.22/6955
• topic: Fractional advection–dispersion equation; Tau method; Shifted Legendre polynomials; Operational matrix; Two-sided Caputo derivative; Riemann–Liouville fractional integral

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.