A high-speed algorithm for computation of fractional differentiation and fractional integration
A high-speed algorithm for computation of fractional differentiation and fractional integration
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DOI：
10.1098/rsta.2012.0152
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
M. Fukunaga;N. Shimizu
中科院分区：
文献类型：
--
作者：
M. Fukunaga;N. Shimizu
提出了一种计算分数阶微分方程中分数阶微分和分数阶积分的高速算法。在该算法中，存储的数据不是要微分或积分的函数，而是函数的加权积分。随着计算时间步长 n 的增加，可以在不损失精度的情况下增加存储器的积分间隔。与标准算法的 n2 不同，计算成本变化为 。
A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n increases. The computing cost varies as , as opposed to n2 of standard algorithms.