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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. | URI: | https://hdl.handle.net/10316/27768 | ISSN: | 0021-9991 | DOI: | 10.1016/j.jcp.2014.08.036 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
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