High-Order Approximation to Caputo Derivatives and Caputo-type Advection-Diffusion Equations: Revisited

被引：23

作者：

Li, Changpin ^{[1
]}

Cai, Min ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Caputo derivative; Caputo-type advection-diffusion equation; convergence; Fourier transform; high-order approximation; 26A33;

D O I：

10.1080/01630563.2017.1291521

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a series of new high-order numerical approximations to -th Caputo derivatives (0<<2) is derived based on a compound of shift operators and high-order approximations to Riemann-Liouville derivatives. The convergence order is independent of the derivative order , rather than the previous error estimates. Several numerical examples including the Caputo-type advection-diffusion equation are displayed, which support the derived numerical schemes.

引用

页码：861 / 890

页数：30

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