Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.22/6955
Título: Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation
Autor: Bhrawy, A. H.
Zaky, M.A.
Machado, J. A. Tenreiro
Palavras-chave: Fractional advection–dispersion equation
Tau method
Shifted Legendre polynomials
Operational matrix
Two-sided Caputo derivative
Riemann–Liouville fractional integral
Data: 2015
Editora: SAGE journals
Relatório da Série N.º: Journal of Vibration and Control;
Resumo: 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.
URI: http://hdl.handle.net/10400.22/6955
DOI: 10.1177/1077546314566835
Versão do Editor: http://jvc.sagepub.com/content/early/2015/01/21/1077546314566835.abstract
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