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

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.