Caputo导数的一种高精度算法及其在扩散现象中的应用  

A high accuracy scheme for the Caputo derivative with an application to diffusion problems

作　　者：吴娟[1] 张华[2] 罗卫华 Wu Juan;Zhang Hua;Luo Weihua(Center of Information and Modern Educational Technology,Hunan University of Arts and Science,Changde,415000,China;School of Mathematics and Physics,Hunan University of Arts and Science,Changde,415000,China)

机构地区：[1]湖南文理学院信息与现代教育技术中心,湖南常德415000 [2]湖南文理学院数理学院,湖南常德415000

出　　处：《湖南文理学院学报（自然科学版）》2023年第4期6-10,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：湖南省自然科学基金(2022JJ30416);湖南省教育厅重点项目(22A0483);湖南文理学院科研项目(17YB04)。

摘　　要：利用二次Lagrange插值函数研究了Caputo分数阶导数算子的一种高精度离散方法,给出了相应的递归公式,证明了该算法的全局数值精度为O(τ^(3-β))。并应用此离散算法对时间分数阶扩散方程进行了数值求解,验证了该算法的可行性和高效性。In this paper,the Caputo fractional derivative is numerically approximated with quadratic Lagrange interpolation function.Corresponding recursion formula is obtained.Theoretical analyses show that this scheme can achieve accuracy of O(τ^(3-β)).To show its practical value,this numerical scheme is used to solve the time fractional diffusion equations.Some numerical examples are given to reflect the efficiency of the proposed method.

关 键 词：CAPUTO导数 扩散问题 LAGRANGE插值 

分 类 号：O241.8[理学—计算数学]