Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4): 1446-1468.doi: 10.1007/s42967-022-00211-3

• ORIGINAL PAPERS • 上一篇    下一篇

Three Kinds of Discrete Formulae for the Caputo Fractional Derivative

Zhengnan Dong, Enyu Fan, Ao Shen, Yuhao Su   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • 收稿日期:2022-06-30 修回日期:2022-08-07 发布日期:2023-12-16
  • 通讯作者: Enyu Fan,E-mail:fanenyu@shu.edu.cn E-mail:fanenyu@shu.edu.cn

Three Kinds of Discrete Formulae for the Caputo Fractional Derivative

Zhengnan Dong, Enyu Fan, Ao Shen, Yuhao Su   

  1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • Received:2022-06-30 Revised:2022-08-07 Published:2023-12-16
  • Contact: Enyu Fan,E-mail:fanenyu@shu.edu.cn E-mail:fanenyu@shu.edu.cn

摘要: In this paper, three kinds of discrete formulae for the Caputo fractional derivative are studied, including the modified L1 discretisation for α ∈ (0, 1), and L2 discretisation and L2C discretisation for α ∈ (1, 2). The truncation error estimates and the properties of the coefficients of all these discretisations are analysed in more detail. Finally, the theoretical analyses are verified by the numerical examples.

关键词: Caputo fractional derivative, Modified L1 discretisation, L2 discretisation, L2C discretisation, Truncation error

Abstract: In this paper, three kinds of discrete formulae for the Caputo fractional derivative are studied, including the modified L1 discretisation for α ∈ (0, 1), and L2 discretisation and L2C discretisation for α ∈ (1, 2). The truncation error estimates and the properties of the coefficients of all these discretisations are analysed in more detail. Finally, the theoretical analyses are verified by the numerical examples.

Key words: Caputo fractional derivative, Modified L1 discretisation, L2 discretisation, L2C discretisation, Truncation error

中图分类号: