Legendre算子矩阵求解分数阶微分方程

摘要

本文考虑用勒让德（Legendre）算子矩阵求解分数阶微分方程的数值解。这种方法是取勒让德多项式的有限项，把勒让德多项式和算子矩阵结合起来，对给定的函数做了有效的离散，将分数阶微分方程转化为代数方程组，使得计算更简便，并给出数值算例验证了方法的有效性。%In this paper, Legendre operator matrix is applied to solve fractional order differential equations. This method is to take the limited items of the Legendre polynomial, which combined the Legendre polynomials with operator matrix. The given function is discretized effectively, the fractional order differential equation is transformed into algebraic equations and computation became convenient. The numerical example shows that the method is effective.