High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations

被引：38

作者：

Li, Zhiqiang ^{[1
]}

Liang, Zongqi ^{[2
]}

Yan, Yubin ^{[3
]}

机构：

[1] LuLiang Univ, Dept Math, Lishi 033000, Peoples R China

[2] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China

[3] Univ Chester, Dept Math, Chester CH1 4BJ, Cheshire, England

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2017年 / 71卷 / 02期

关键词：

Time fractional partial differential equations; Finite element method; Error estimates; FINITE DIFFERENCE/SPECTRAL APPROXIMATIONS; DIFFUSION-EQUATIONS; CAPUTO DERIVATIVES; STABILITY;

D O I：

10.1007/s10915-016-0319-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce a new numerical method for solving time fractional partial differential equation. The time discretization is based on Diethelm's method where the Hadamard finite-part integral is approximated by using the piecewise quadratic interpolation polynomials. The space discretization is based on the standard finite element method. The error estimates with the convergence order are proved in detail by using the argument developed recently by Lv and Xu (SIAM J Sci Comput 38:A2699-A2724, 2016), where and h denote the time and space step sizes, respectively. Numerical examples in both one- and two-dimensional cases are given.

引用

页码：785 / 803

页数：19

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