Abstract
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.
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Acknowledgements
The modified L1, L2, and L2C discretisations for Caputo fractional derivatives are the graduation projects of Yuhao Su, Zhengnan Dong, and Ao Shen under the guidance of Professor Changpin Li. Dr. Enyu Fan has improved their works. Prof. Zhizhong Sun has read the original paper carefully and given valuable suggestions for revision.
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Dong, Z., Fan, E., Shen, A. et al. Three Kinds of Discrete Formulae for the Caputo Fractional Derivative. Commun. Appl. Math. Comput. 5, 1446–1468 (2023). https://doi.org/10.1007/s42967-022-00211-3
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DOI: https://doi.org/10.1007/s42967-022-00211-3
Keywords
- Caputo fractional derivative
- Modified L1 discretisation
- L2 discretisation
- L2C discretisation
- Truncation error