dc.contributor.author Mustapha, K. dc.contributor.author Furati, K. dc.contributor.author Knio, Omar dc.contributor.author Maitre, O. Le dc.date.accessioned 2017-12-28T07:32:10Z dc.date.available 2017-12-28T07:32:10Z dc.date.issued 2017-06-03 dc.identifier.uri http://hdl.handle.net/10754/626452 dc.description.abstract Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates. dc.publisher arXiv dc.relation.url http://arxiv.org/abs/1706.00971v1 dc.relation.url http://arxiv.org/pdf/1706.00971v1 dc.rights Archived with thanks to arXiv dc.title A finite difference method for space fractional differential equations with variable diffusivity coefficient dc.type Preprint dc.contributor.department Applied Mathematics and Computational Science Program dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.eprint.version Pre-print dc.contributor.institution Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia dc.contributor.institution CNRS, LIMSI, Universit´e Paris-Scalay, Campus Universitaire - BP 133, F-91403 Orsay, France dc.identifier.arxivid arXiv:1706.00971 kaust.person Knio, Omar kaust.grant.number KAUST005 refterms.dateFOA 2018-06-13T11:10:33Z
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