Moving finite element methods for time fractional partial differential equations
With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and...
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| Published in | Science China. Mathematics Vol. 56; no. 6; pp. 1287 - 1300 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
SP Science China Press
01.06.2013
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| Online Access | Get full text |
| ISSN | 1674-7283 1869-1862 |
| DOI | 10.1007/s11425-013-4584-2 |
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| Abstract | With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method. |
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| AbstractList | With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuniform meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations (FPDEs). The unconditional stability and convergence rates of 2- alpha for time and r for space are proved when the method is used for the linear time FPDEs with alpha -th order time derivatives. Numerical examples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method. With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method. With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuniform meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations (FPDEs). The unconditional stability and convergence rates of 2 − α for time and r for space are proved when the method is used for the linear time FPDEs with α -th order time derivatives. Numerical examples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method. |
| Author | JIANG YingJun MA JingTang |
| AuthorAffiliation | Department of Mathematics and Scientific Computing, Changsha University of Science and Technology, Changsha 410076, China School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China |
| Author_xml | – sequence: 1 givenname: YingJun surname: Jiang fullname: Jiang, YingJun email: jiangyingjun@csust.edu.cn organization: Department of Mathematics and Scientific Computing, Changsha University of Science and Technology – sequence: 2 givenname: JingTang surname: Ma fullname: Ma, JingTang organization: School of Economic Mathematics, Southwestern University of Finance and Economics |
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| Cites_doi | 10.1007/s11075-010-9379-8 10.1137/0731038 10.1007/978-1-4419-7916-2 10.1137/080718942 10.1007/s11425-010-3128-2 10.1016/j.amc.2006.08.163 10.1016/S0021-9991(02)00040-2 10.1023/A:1016592219341 10.1007/s11425-010-4133-1 10.1137/060673114 10.1007/s11075-008-9258-8 10.1016/j.cam.2011.01.011 10.1137/0517050 10.1016/j.jcp.2007.02.001 10.1007/s11425-010-4075-7 10.1016/j.jcp.2007.05.012 10.1016/j.jmaa.2005.03.054 10.1016/S0370-1573(00)00070-3 10.1007/978-1-4757-3658-8 10.1023/B:NUMA.0000027736.85078.be 10.1016/j.cam.2008.04.005 |
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| Notes | fractional partial differential equations, moving finite element methods, blow-up solutions With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations （FPDEs）. The unconditional stability and convergence rates of 2 -a for time and r for space are proved when the method is used for the linear time FPDEs with a-th order time derivatives. Numerical exam-ples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method. 11-1787/N ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| Snippet | With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuni- form meshes both in time and in space, is proposed in this... With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuniform meshes both in time and in space, is proposed in this... |
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| SubjectTerms | Applications of Mathematics China Computer simulation Convergence Derivatives Finite element method Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Partial differential equations 偏微分方程 分数阶 和空间 时间导数 有限元方法 爆破解 移动 线性时间 |
| Title | Moving finite element methods for time fractional partial differential equations |
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