Numerical methods for fractional partial differential equations

被引：103
|
作者：
Li, Changpin [1 ]
Chen, An [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2018年 / 95卷 / 6-7期
基金：
中国国家自然科学基金;
关键词：
Finite difference methods; Galerkin finite element methods; spectral methods; fast algorithms; fractional partial differential equations; FINITE-ELEMENT-METHOD; DISCONTINUOUS GALERKIN METHODS; SPECTRAL COLLOCATION METHOD; DIFFUSION-WAVE EQUATION; BOUNDARY-VALUE-PROBLEMS; COMPACT ADI SCHEME; HIGH-ORDER APPROXIMATION; DISTRIBUTED-ORDER; NONLOCAL DIFFUSION; DIFFERENCE/SPECTRAL APPROXIMATIONS;
D O I：
10.1080/00207160.2017.1343941
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this review paper, we are mainly concerned with the finite difference methods, the Galerkin finite element methods, and the spectral methods for fractional partial differential equations (FPDEs), which are divided into the time-fractional, space-fractional, and space-time-fractional partial differential equations (PDEs). Besides, fast algorithms for the FPDEs are included in order to stimulate more efficient algorithms for high-dimensional FPDEs.
引用
收藏
页码：1048 / 1099
页数：52
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