A backward euler orthogonal spline collocation method for the time‐fractional Fokker–Planck equation |
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| Authors: | Graeme Fairweather Haixiang Zhang Xuehua Yang Da Xu |
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| Affiliation: | 1. Mathematical Reviews, American Mathematical Society, Ann Arbor, Michigan;2. School of Science, Hunan University of Technology, Hunan, People's Republic of China;3. Department of Mathematics, Hunan Normal University, Changsha, People's Republic of China |
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| Abstract: | We formulate and analyze a novel numerical method for solving a time‐fractional Fokker–Planck equation which models an anomalous subdiffusion process. In this method, orthogonal spline collocation is used for the spatial discretization and the time‐stepping is done using a backward Euler method based on the L1 approximation to the Caputo derivative. The stability and convergence of the method are considered, and the theoretical results are supported by numerical examples, which also exhibit superconvergence. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1534–1550, 2015 |
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| Keywords: | time‐fractional Fokker– Planck equation orthogonal spline collocation method Caputo derivative backward Euler method stability, convergence superconvergence |
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