时间分数阶色散方程的高阶差分方法

High Order Finite Difference Method for the Time Fractional Dispersive Equation

时间分数阶色散方程用以描述带有记忆性的色散现象。本文研究分数阶色散方程的高精度差分方法,利用紧致差分格式的构造技巧,得到了求解时间分数阶色散方程的四点四阶和五点六阶2个紧致隐式差分格式,收敛阶分别为O(τ2+h4)和O(τ2+h6).数值算例表明本文方法是高精度有效的,且具有很好的数值稳定性。

The time fractional dispersive equation is used to model the phenomena of dispersions with memory. By using the techniques of compact schemes, fourth-order four-point stencil and sixth-order fivepoint stencil compact implicit difference schemes were derived for the time fractional dispersive equation. It was shown that the convergence rate of the two compact implicit difference schemes were O（τ^2 -h^4） and O（τ^2＋h^6）,respectively. The numerical experiments show that the present compact schemes are effective and with high accuracy.