一类Caputo-Hadamard分数阶常微分方程数值解法
A Caputo-Hadamard Numerical Solution for Fractional Ordinary Differential Equations
DOI: 10.12677/AAM.2024.133087, PDF, 下载: 48  浏览: 102 
作者: 曹齐：长沙理工大学，数学与统计学院，湖南 长沙
关键词: Caputo-Hadamard导数；L2 ? 1σ 格式；非均匀网格；有限差分法；Caputo-Hadamard Derivative； L2 ? 1σ Format； Heterogeneous Grid； Finite Difference Method
摘要: 本文采用有限差分法求解一类带有Caputo-Hadamard分数阶导数的常微分方程，我们用构造 的L2 − 1σ 公式来近似方程中的Caputo-Hadamard 分数阶导数，并在特殊非均匀网格(对数意义 下的均匀网格)上采用有限差分法离散。 实验结果表明，该方法得到的收敛速度为(3 − α)阶。
Abstract: In this paper, the finite difference method is used to solve a class of ordinary differential equations with Caputo-Hadamard fractional derivative. We approximate the Caputo- Hadamard fractional derivative by using the constructed L2 − 1σ formula. The finite difference method is used to discrete the special inhomogeneous mesh (uniform mesh in logarithmic sense). The experimental results show that the convergence rate obtained by this method is (3 − α).
文章引用：曹齐. 一类Caputo-Hadamard分数阶常微分方程数值解法[J]. 应用数学进展, 2024, 13(3): 928-933. https://doi.org/10.12677/AAM.2024.133087

参考文献

[1] Li, C., Li, Z. and Wang, Z. (2020). Mathematical Analysis and the Local Discontinuous Galerkin Method for Caputo-Hadamard Fractional Partial Differential Equation. Journal of Scientific Computing, 85, Article No. 41.
https://doi.org/10.1007/s10915-020-01353-3
[2] Li, C. and Li, Z. (2021). Asymptotic Behaviours of Solution to Caputo-Hadamard Fractional Partial Differential Equation with Fractional Laplacian. International Journal of Computer Mathematics, 98, 305-339.
https://doi.org/10.1080/00207160.2020.1744574
[3] Yin, C., Li, C. and Bi, Q. (2018). Approximation to Hadamard Derivative via the Finite Part Integral. Entropy, 20, Article 983.
https://doi.org/10.3390/e20120983
[4] Gohar, M., Li, C. and Li, Z. (2020). Finite Difference Methods for Caputo-Hadamard Fractional Differential Equations. Mediterranean Journal of Mathematics, 17, Article No. 194.
https://doi.org/10.1007/s00009-020-01605-4
[5] Alikhanov, A. A. (2015). A New Difference Scheme for the Time Fractional Diffusion Equation. Journal of Computational Physics, 280, 424-438.
https://doi.org/10.1016/j.jcp.2014.09.031

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