分数阶微分方程的Haar小波算法研究

Study on the Haar wavelet algorithm of fractional differential equations

在BPFs的Caputo分数阶微分算子矩阵的基础上,建立了Haar小波的分数阶微分算子矩阵,提出了一种有效的求解分数阶微分方程的Haar小波数值方法,并将该方法应用于线性和非线性分数阶常微分方程求解中。数值算例表明,该算法简单,数值精确度高,是一种高效的数值求解方法。

In this paper,the Haar wavelet operational matrix of Caputo fractional derivative is estaollsneu based on the BPF operational matrix, and an efficient Haar wavelet numerical method for solving fractional differential equations is proposed. The method is applied to solve linear and nonlinear fractional ordinary differential equations. And numerical examples results demonstrate that the algorithm is simple, precise and highly efficient.