α阶右侧Caputo分数阶导数的高阶插值逼近  

The Higher-Order Interpolation Approximation of the Right Side of Caputo Fractional Derivative

作　　者：闫羽媛 梁宗旗[1] YAN Yuyuan;LIANG Zongqi(School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2021年第4期365-373,共9页Journal of Jimei University：Natural Science

基　　金：国家自然科学基金项目(11201178,11901237);福建省自然科学基金项目(2019J01329);福建省教育厅项目(JT180262,ZC2018008)。

摘　　要：对α阶(1<α<2)右侧Caputo分数阶导数引入新变量以降低函数阶数,采用L2-1插值方法,得到了高阶插值格式。为了进一步改善L2-1方法在区间[t N-1,b]上由L1插值带来的非一致O(Δt 4-α)阶精度,增加约束条件,使整体区间均利用L2插值得到一致的O(Δt 4-α)精度的高阶插值格式,并分别证明了二者的截断误差。In this paper,a new variable to reduce the order of the function for the fractional derivative of Caputo on the right side ofα(1<α<2)was introduced,and L2-1 interpolation method was used to obtain the higher-order interpolation scheme.In order to further improve the non-uniform O(Δt 4-α)order accuracy of L2-1 method on the interval[t N-1,b]brought by L 1 interpolation,by increasing the constraint conditions,the whole interval was made use of L2 interpolation to obtain the consistent O(Δt 4-α)high-order interpolation format,and the truncation errors of both were proved respectively.

关 键 词：CAPUTO分数阶导数 L2-1插值 L 2插值 收敛阶 

分 类 号：O241.82[理学—计算数学]