A backward euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation

被引：21

作者：

Fairweather, Graeme ^{[1
]}

Zhang, Haixiang ^{[2
]}

Yang, Xuehua ^{[2
]}

Xu, Da ^{[3
]}

机构：

[1] Amer Math Soc, Math Reviews, Ann Arbor, MI 48103 USA

[2] Hunan Univ Technol, Sch Sci, Zhuzhou 412008, Hunan, Peoples R China

[3] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 31卷 / 05期

关键词：

time-fractional Fokker-Planck equation; orthogonal spline collocation method; Caputo derivative; backward Euler method; stability; convergence; superconvergence; FINITE-DIFFERENCE APPROXIMATIONS; DIAGONAL LINEAR-SYSTEMS; MODIFIED ALTERNATE ROW; NUMERICAL-SOLUTION; FORTRAN PACKAGES; SPACE; DIFFUSION; ALGORITHM; FLOW;

D O I：

10.1002/num.21958

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1534-1550, 2015

引用

页码：1534 / 1550

页数：17

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