Three Kinds of Discrete Formulae for the Caputo Fractional Derivative
Zhengnan Dong , Enyu Fan , Ao Shen , Yuhao Su
Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4) : 1446 -1468.
In this paper, three kinds of discrete formulae for the Caputo fractional derivative are studied, including the modified L1 discretisation for $\alpha \in (0,1)$, and L2 discretisation and L2C discretisation for $\alpha \in (1,2)$. 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.
/
| 〈 |
|
〉 |
PDF
