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• W3175431913 abstract "Abstract A second-order accurate time-stepping 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 semidiscrete 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 time-stepping scheme 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." @default.
• W3175431913 created "2021-07-05" @default.
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• W3175431913 date "2022-07-26" @default.
• W3175431913 modified "2023-10-16" @default.
• W3175431913 title "A second-order accurate numerical scheme for a time-fractional Fokker–Planck equation" @default.
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• W3175431913 doi "https://doi.org/10.1093/imanum/drac031" @default.
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