Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

L.B. Feng, P. Zhuang, F. Liu and I. Turner

Applied Mathematics and Computation, 2015, vol. 257, issue C, 52-65

Abstract: In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Keywords: Finite volume method; Variable coefficients; Riesz fractional derivative; Fractional diffusion equation; Nodal basis functions; Stability and convergence (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:52-65

DOI: 10.1016/j.amc.2014.12.060

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