Bernoulli算子矩阵求解分数阶微分方程的数值解  

Numerical Solutions of Fractional Differential Equations by Bernoulli Operator Matrix

作　　者：杨晓丽 许雷[2] YANG Xiaoli;XU Lei(School of Life Sciences,Neijiang Normal University,Neijiang, Sichuan 641199,China;School of Mathematics and Information Science,Neijiang Normal University,Neijiang, Sichuan 641199,China)

机构地区：[1]内江师范学院生命科学学院,四川内江641199 [2]内江师范学院数学与信息科学学院,四川内江641199

出　　处：《西昌学院学报（自然科学版）》2019年第2期55-58,共4页Journal of Xichang University(Natural Science Edition)

基　　金：四川省教育厅资助项目(17ZB0220)

摘　　要：提出了一种基于伯努利(Bernoulli)多项式的分数阶微分方程数值求解的新方法,推导了分数导数的Bernoulli运算矩阵,结合Tau法和配方法将分数阶微分方程简化为代数方程组。通过实例说明了该方法的有效性和适用性。This paper presents a new numerical method for solving fractional differential equations based on Bernoulli polynomials. Bernoulli operation matrix of fractional derivative is deduced, and fractional differential equations are simplified to algebraic equations by combining Tau and collocation methods. The validity and applicability of this method are illustrated by examples.

关 键 词：伯努利多项式 分数阶导数 算子矩阵 

分 类 号：O241.8[理学—计算数学]