α阶右侧Caputo分数阶导数的高阶插值逼近-《集美大学学报（自然科学版）》

文章信息/Info

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

Author(s):: YAN Yuyuan; LIANG Zongqi; (School of Science,Jimei University,Xiamen 361021,China)

Keywords:: fractional derivative of Caputo; L2-1interpolation; L2 interpolation; order of convergence

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[tN-1，b]上由L1插值带来的非一致O(Δt4-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(Δt4-α)精度的高阶插值格式,并分别证明了二者的截断误差。

Abstract:: In this paper,a new variable to reduce the order of the function for the fractional derivative of Caputo on the right side of α(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(Δt4-α) order accuracy of L2-1 method on the interval [tN-1,b] brought by L1 interpolation,by increasing the constraint conditions,the whole interval was made use of L2 interpolation to obtain the consistent O(Δt4-α) high-order interpolation format,and the truncation errors of both were proved respectively.