A PRECONDITIONED FAST FINITE DIFFERENCE METHOD FOR SPACE-TIME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

被引：39

作者：

Fu, Hongfei ^{[1
]}

Wang, Hong ^{[2
]}

机构：

[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2017年 / 20卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

anomalous diffusion; finite difference method; space-time discretization; space-time fractional diffusion equation; Krylov subspace method; ELEMENT-METHOD; NUMERICAL ALGORITHMS; DIFFUSION-EQUATIONS; ADVECTION; APPROXIMATIONS; DISPERSION; CONVERGENCE; STABILITY; CALCULUS;

D O I：

10.1515/fca-2017-0005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a fast space-time finite difference method for space-time fractional diffusion equations by fully utilizing the mathematical structure of the scheme. A circulant block preconditioner is proposed to further reduce the computational costs. The method has optimal-order memory requirement and approximately linear computational complexity. The method is not lossy, as no compression of the underlying numerical scheme has been employed. Consequently, the method retains the stability, accuracy, and, in particular, the conservation property of the underlying numerical scheme. Numerical experiments are presented to show the efficiency and capacity of long time modelling of the new method.

引用

页码：88 / 116

页数：29

共 50 条

[41] Exponential rational function method for space-time fractional differential equations
Aksoy, Esin
Kaplan, Melike
Bekir, Ahmet
WAVES IN RANDOM AND COMPLEX MEDIA, 2016, 26 (02) : 142 - 151
[42] The generalized bifurcation method for deriving exact solutions of nonlinear space-time fractional partial differential equations
Wen, Zhenshu
APPLIED MATHEMATICS AND COMPUTATION, 2020, 366
[43] The modified generalized Kudryashov method for nonlinear space-time fractional partial differential equations of Schrodinger type
Liu, Fushun
Feng, Yuqiang
RESULTS IN PHYSICS, 2023, 53
[44] An advanced method with convergence analysis for solving space-time fractional partial differential equations with multi delays
Kurkcu, Omur Kivanc
Aslan, Ersin
Sezer, Mehmet
EUROPEAN PHYSICAL JOURNAL PLUS, 2019, 134 (08):
[45] An advanced method with convergence analysis for solving space-time fractional partial differential equations with multi delays
Ömür Kıvanç Kürkçü
Ersin Aslan
Mehmet Sezer
The European Physical Journal Plus, 134
[46] A Finite Difference Method for Space Fractional Differential Equations with Variable Diffusivity Coefficient
K. A. Mustapha
K. M. Furati
O. M. Knio
O. P. Le Maître
Communications on Applied Mathematics and Computation, 2020, 2 : 671 - 688
[47] A Finite Difference Method for Space Fractional Differential Equations with Variable Diffusivity Coefficient
Mustapha, K. A.
Furati, K. M.
Knio, O. M.
Le Maitre, O. P.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2020, 2 (04) : 671 - 688
[48] Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations
Huang, Yun-Chi
Lei, Siu-Long
NUMERICAL ALGORITHMS, 2020, 84 (01) : 37 - 62
[49] Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations
Yun-Chi Huang
Siu-Long Lei
Numerical Algorithms, 2020, 84 : 37 - 62
[50] A SPACE-TIME MULTIGRID METHOD FOR PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS
HORTON, G
VANDEWALLE, S
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1995, 16 (04): : 848 - 864

← 1 2 3 4 5 →