小波方法求一类变系数分数阶微分方程数值解

Wavelet method to the numerical solution for a class of fractional differential equation with variable coefficients

考虑一类变系数分数阶微分方程的数值解.将Haar小波与算子矩阵思想有效结合,并对变系数进行恰当的离散,将变系数分数阶微分方程转化为线性代数方程组,使得计算更简便,并证明了该算法的收敛性.最后通过数值算例验证了方法的有效性.

A wavelet method to the numerical solution for a class of fractional differential equation with variable coefficients is proposed,which combining Haar wavelet and operational matrix together and discreting the coefficients efficaciously.The original problem is translated into a system of algebraic equations and the computation become convenient.The convergence of this method is given.The numerical examples show that the method is effective.