非标准有限差分法求解时滞抛物型方程

Nonstandard Finite Difference Method for Delay Parabolic Equation

提出求解时滞抛物型方程的非标准有限差分法,其特点是在对微分方程中关于时间一阶导数项进行离散时,利用时间步长的函数φ(Δt)代替分母Δt,通过稳定性分析可以看出该格式是条件稳定的,数值算例表明该方法有很高的精度。

This paper proposes the nonstandard finite difference （NSFD） method to solve the de-lay parabolic equation which replaces the denominator △t by the time step function φ（△t） for a discrete time derivative in a differential equation. Stability analysis proves that the format is con-ditionally stable and numerical examples show that this method has high accuracy.