一类变时间分数阶扩散方程的Chebyshev小波数值法

Numerical Solution of the Variable Order Time Fractional Diffusion Equation Using Chebyshev Wavelets

运用第二类Chebyshev小波函数拟合的方法,求解一类变时间分数阶扩散方程。通过推导得出第二类Chebyshev小波的变阶微分算子矩阵,进而利用算子矩阵将方程转化为一组线性方程组,再利用最小二乘的方法求得方程组的解,进而得到原方程的数值解。并给出数值算例验证了本方法的有效性。

This paper presents an estimation method to calculate the variable order time fractional diffusion equation using the second kind Chebyshev wavelets function. The proposed operational matrixes of the second kind Chebyshev wavelet （SCW） is utilized to transform the fractional equation to a set of linear equations. Method of least square is used to solve the set of linear equations. The accuracy and performance of the method is demonstrated by numerical examples.