时间分数阶色散方程的有限差分方法

A finite difference method for the time fractional dispersive equation

提出求解时间分数阶色散方程的一类隐式差分格式,并证明其无条件稳定性和收敛性,收敛阶为O(τ+h2)。该分数阶色散方程是将一般的色散方程中的时间一阶导数用α(0<α<1)阶导数代替所得到的。数值算例表明本方法是有效的。

An implicit difference scheme for solving the time fractional dispersive equation is presented.It is shown that the method is unconditional stable and the convergence order of the method is O（τ＋h2）.The fractional dispersive equation is obtained from the classical dispersive equation by replacing the first order time derivative with fractional derivative of order α（0α1）.Finally,the numerical example shows that the presented implicit difference method is effective.