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Title: An explicit high order method for fractional advection diffusion equations
Authors: Sousa, Ercília 
Keywords: Higher order methods; Fractional differential equations; Finite differences; Advection diffusion equations
Issue Date: 1-Dec-2014
Publisher: Elsevier
Citation: SOUSA, Ercília - An explicit high order method for fractional advection diffusion equations. "Journal of Computational Physics". ISSN 0021-9991. Vol. 278 (2014) p. 257–274
Serial title, monograph or event: Journal of Computational Physics
Volume: 278
Abstract: We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1<α≤2. This operator is defined by a combination of the left and right Riemann–Liouville fractional derivatives. We study the convergence of the numerical method through consistency and stability. The order of convergence varies between two and three and for advection dominated flows is close to three. Although the method is conditionally stable, the restrictions allow wide stability regions. The analysis is confirmed by numerical examples.
ISSN: 0021-9991
DOI: 10.1016/
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais
FCTUC Matemática - Artigos em Revistas Internacionais

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