Multi-Domain Decomposition Pseudospectral Method for Nonlinear Fokker-Planck Equations

doi:10.1007/s42967-019-00013-0

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (2): 231-252.doi: 10.1007/s42967-019-00013-0

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Multi-Domain Decomposition Pseudospectral Method for Nonlinear Fokker-Planck Equations

Tao Sun¹, Tian-jun Wang²

1 School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China;
2 School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

收稿日期:2018-05-01 修回日期:2018-11-11 出版日期:2019-06-20 发布日期:2019-06-20
通讯作者: Tian-jun Wang, Tao Sun E-mail:wangtianjun64@163.com;sunt@lixin.edu.cn
基金资助:
The work of Tao Sun is supported in part by the NSF of China (Grant numbers 11401380, 11671166 and 11701371). The work of Tian-jun Wang is supported in part by the NSF of China (Grant numbers 11371123, 11571151 and 11771299).

Multi-Domain Decomposition Pseudospectral Method for Nonlinear Fokker-Planck Equations

Tao Sun¹, Tian-jun Wang²

1 School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China;
2 School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

Received:2018-05-01 Revised:2018-11-11 Online:2019-06-20 Published:2019-06-20
Contact: Tian-jun Wang, Tao Sun E-mail:wangtianjun64@163.com;sunt@lixin.edu.cn
Supported by:
The work of Tao Sun is supported in part by the NSF of China (Grant numbers 11401380, 11671166 and 11701371). The work of Tian-jun Wang is supported in part by the NSF of China (Grant numbers 11371123, 11571151 and 11771299).

摘要/Abstract

摘要： Results on the composite generalized Laguerre-Legendre interpolation in unbounded domains are established. As an application, a composite Laguerre-Legendre pseudospectral scheme is presented for nonlinear Fokker-Planck equations on the whole line. The convergence and the stability of the proposed scheme are proved. Numerical results show the efciency of the scheme and conform well to theoretical analysis.

关键词: Composite generalized Laguerre-Legendre pseudospectral approximation, Nonlinear Fokker-Planck equations defned on unbounded domains, Multi-domain decomposition pseudospectral method

Abstract: Results on the composite generalized Laguerre-Legendre interpolation in unbounded domains are established. As an application, a composite Laguerre-Legendre pseudospectral scheme is presented for nonlinear Fokker-Planck equations on the whole line. The convergence and the stability of the proposed scheme are proved. Numerical results show the efciency of the scheme and conform well to theoretical analysis.

Key words: Composite generalized Laguerre-Legendre pseudospectral approximation, Nonlinear Fokker-Planck equations defned on unbounded domains, Multi-domain decomposition pseudospectral method

中图分类号:

Tao Sun, Tian-jun Wang. Multi-Domain Decomposition Pseudospectral Method for Nonlinear Fokker-Planck Equations[J]. Communications on Applied Mathematics and Computation, 2019, 1(2): 231-252.

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Multi-Domain Decomposition Pseudospectral Method for Nonlinear Fokker-Planck Equations

Multi-Domain Decomposition Pseudospectral Method for Nonlinear Fokker-Planck Equations

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