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dc.contributor.authorMustapha, Kassem
dc.contributor.authorKnio, Omar
dc.contributor.authorMaître, Olivier P. Le
dc.date.accessioned2021-07-14T06:48:53Z
dc.date.available2021-07-14T06:48:53Z
dc.date.issued2021-06-27
dc.identifier.urihttp://hdl.handle.net/10754/670201
dc.description.abstractA time-stepping $L1$ scheme for solving a time fractional Fokker-Planck equation of order $\alpha \in (0, 1)$, with a general driving force, is investigated. A stability bound for the semi-discrete solution is obtained for $\alpha\in(1/2,1)$ {via a novel and concise approach.} Our stability estimate is $\alpha$-robust in the sense that it remains valid in the limiting case where $\alpha$ approaches $1$ (when the model reduces to the classical Fokker-Planck equation), a limit that presents practical importance. Concerning the error analysis, we obtain an optimal second-order accurate estimate for $\alpha\in(1/2,1)$. A time-graded mesh is used to compensate for the singular behavior of the continuous solution near the origin. The $L1$ scheme is associated with a standard spatial Galerkin finite element discretization to numerically support our theoretical contributions. We employ the resulting fully-discrete computable numerical scheme to perform some numerical tests. These tests suggest that the imposed time-graded meshes assumption could be further relaxed, and we observe second-order accuracy even for the case $\alpha\in(0,1/2]$, that is, outside the range covered by the theory.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2106.14146.pdf
dc.rightsArchived with thanks to arXiv
dc.titleA second-order accurate numerical scheme for a time-fractional Fokker-Planck equation
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.arxivid2106.14146
kaust.personKnio, Omar
refterms.dateFOA2021-07-14T06:49:13Z


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