空间分数阶扩散方程的谱及拟谱方法

Spectral and Psedo-Spectral Method for Space Fractional Diffusion Equations

本文研究了空间分数阶扩散方程的数值解法.首先,利用Galerkin谱方法对方程在空间方向进行离散,然后,利用θ-方法对时间变量进行离散.利用能量方法,得到了全离散方程解的稳定性及误差估计.数值结果表明拟谱方法求解分数阶扩散方程数值解高精度和有效性.

This paper investigates a numerical scheme for solving space fractional diffusion equations （SFDEs） based on spectral and pseudo-spectral method. The equation is firstly discretized in space variable x by using the Galerkin spectral method. And then, 0-method is employed to discretize the time variable t. The stability and error estimate for the approx- imation solution of the full discretized equation are derived by energe methods. Numerical examples show a good agreement with the theoretical anlysis.