Caputo型线性分数阶常微分方程的一种新的高阶数值方法  

A New Numerical Algorithm for Caputo-type Linear Fractional Order Differential Equations

作　　者：朱鹏程 Zhu Pengcheng(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《科学技术创新》2022年第34期35-39,共5页Scientific and Technological Innovation

摘　　要：通过分段的三次插值公式近似Caputo型分数阶导数,从而构造了线性分数阶常微分方程的高阶数值格式,接着给出了构造的数值格式的截断局部误差估计,在最后部分我们举出数值算例证明理论分析的正确性。The high order numerical format of the linear fractional ordinary differential equation is constructed by approximating the Caputo-type fractional derivative by the cubic interpolation formula of the segment, and then gives the local truncation error estimate of the construction format, and finally we further verify the validity of the numerical through the relevant numerical expeiments.

关 键 词：线性分数阶常微分 分段三次插值 高阶数值格式 

分 类 号：O241.82[理学—计算数学]