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

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。

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).