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dc.contributor.authorMustapha, K.
dc.contributor.authorFurati, K.
dc.contributor.authorKnio, Omar
dc.contributor.authorMaitre, O. Le
dc.date.accessioned2017-12-28T07:32:10Z
dc.date.available2017-12-28T07:32:10Z
dc.date.issued2017-06-03
dc.identifier.urihttp://hdl.handle.net/10754/626452
dc.description.abstractAnomalous 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.publisherarXiv
dc.relation.urlhttp://arxiv.org/abs/1706.00971v1
dc.relation.urlhttp://arxiv.org/pdf/1706.00971v1
dc.rightsArchived with thanks to arXiv
dc.titleA finite difference method for space fractional differential equations with variable diffusivity coefficient
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia
dc.contributor.institutionCNRS, LIMSI, Universit´e Paris-Scalay, Campus Universitaire - BP 133, F-91403 Orsay, France
dc.identifier.arxividarXiv:1706.00971
kaust.personKnio, Omar
kaust.grant.numberKAUST005
refterms.dateFOA2018-06-13T11:10:33Z


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