## 留言板

 引用本文: 高兴华, 李宏, 刘洋. 非线性分数阶常微分方程的分段线性插值多项式方法[J]. 应用数学和力学, 2021, 42(5): 531-540.
GAO Xinghua, LI Hong, LIU Yang. A Piecewise Linear Interpolation Polynomial Method for Nonlinear Fractional Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 531-540. doi: 10.21656/1000-0887.410149
 Citation: GAO Xinghua, LI Hong, LIU Yang. A Piecewise Linear Interpolation Polynomial Method for Nonlinear Fractional Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 531-540.

## 非线性分数阶常微分方程的分段线性插值多项式方法

##### doi: 10.21656/1000-0887.410149

###### 作者简介:高兴华(1991—)，女，博士生(E-mail: gaoxinghua1991@126.com);李宏(1973—)，女，教授，博士生导师(通讯作者. E-mail: smslh@imu.edu.cn).
• 中图分类号: O241.82

## A Piecewise Linear Interpolation Polynomial Method for Nonlinear Fractional Ordinary Differential Equations

Funds: The National Natural Science Foundation of China（11761053;11661058）
• 摘要: 通过分段线性插值多项式方法构造了一类含有Hadamard有限部分积分的非线性常微分方程的数值离散格式.在时间方向上, 利用分段线性插值多项式方法对分数阶导数项进行近似, 并通过二阶向后差分格式来离散整数阶导数项.经过详细的证明, 得到了收敛精度为O(τmin{1+α,1+β})的误差估计结果.最后,通过数值算例和理论结果的对比直观地说明了理论分析的正确性.
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##### 出版历程
• 收稿日期:  2020-05-26
• 修回日期:  2020-11-16
• 刊出日期:  2021-05-01

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