针对阶数 α∈(1,2) 且带 Caputo 导数的分数阶 Dirichlet 型边值问题的打靶法
Shooting Methods for Fractional Dirichlet-Type Boundary Value Problems of Order $α\in (1,2)$ With Caputo Derivatives
AI总结：
本文针对带 Caputo 导数的非线性分数阶 Dirichlet 型边值问题，提出采用比例分割打靶法选取初始值，证明其可在极少数迭代内达到高精度收敛，并给出相应理论解释。
摘要：
对于与阶数 α∈(1,2) 且使用 Caputo 导数的非线性分数阶微分方程相关的 Dirichlet 型边值问题的数值求解，我们建议采用打靶法。特别地，我们证明，所谓的选择所需初始值的比例分割技术能够使数值格式在极少的打靶迭代次数内收敛到高精度，并且我们为这种良好的数值行为提供了分析背景的解释。
英文摘要：
For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $α\in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we demonstrate that the so-called proportional secting technique for selecting the required initial values leads to numerical schemes that converge to high accuracy in a very small number of shooting iterations, and we provide an explanation of the analytical background for this favourable numerical behaviour.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
