求解时间分数阶二维扩散方程的交替方向隐式法

An Alternating Direct Implicit Method for Time- Fractional Diffusion Equation in Two Space Dimensions

采用交替方向思想数值模拟时间分数阶二维扩散方程初边值问题，构造出计算简单且稳定性好的交替方向隐式离散格式。借助傅里叶分析技术，证明了离散格式的无条件稳定性，并证明了格式关于时间与空间具有最优收敛精度。数值实验支持了文中理论结果。

In this paper, an alternating direct implicit method is proposed to approximate a kind of time-fractional diffusion equation, which possesses simple calculation and higher stability. By means of the Fourier analysis, the unconditional stability of discretization schemes as well as the optimal convergence accuracy of the format concerning the time and space has been verified.