A high-order numerical scheme for the impulsive fractional ordinary differential equations
A high-order numerical scheme for the impulsive fractional ordinary differential equations
复制标题
脉冲分数常微分方程的高阶数值格式
DOI：
10.1080/00207160.2017.1398322
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发表时间：
2018
影响因子：
1.8
通讯作者：
Ziqiang Wang
中科院分区：
文献类型：
--
作者：
Junying Cao;Lizhen Chen;Ziqiang Wang
本文利用一种很好的技巧构造了脉冲分数阶常微分方程组的高阶数值格式。这种方法是基于积分方程组的一种常用方法--逐块法。在我们的方法中，改进了经典的逐块方法，以避免在每个块步骤中未知解的耦合，但相邻两个脉冲点之间的前两步除外。给出了该格式的收敛和稳定性分析。证明了数值解收敛到3+qfor阶的精确解，其中q是分数导数的阶数。文中给出了一系列数值算例，支持了理论结果。
In this paper, we use a good technique to construct a high-order numerical scheme for the impulsive fractional ordinary differential equations (IFODEs). This technique is based on the so-called block-by-block method, which is a common method for the integral equations. In our approach, the classical block-by-block method is improved so as to avoid the coupling of the unknown solutions at each block step with an exception in the first two steps between two adjacent pulse points. The convergence and stability analysis of the scheme are given. It proves that the numerical solution converges to the exact solution with order 3+qfor, whereqis the order of the fractional derivative. A series of numerical examples are provided to support the theoretical results.