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

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.