二阶延迟微分方程Runge-Kutta方法的稳定性

The stability of Runge-Kutta method for the second order delay differential equations

研究二阶延迟微分方程Runge-Kutta方法的稳定性.首先,引入新变量,将二阶延迟微分方程化为一阶方程组.然后,应用Runge-Kuta方法于一阶方程组,给出了Runge-Kutta稳定的充分条件,进而得到了二阶延迟微分方程Runge-Kutta方法稳定的充分条件.最后,通过数值试验验证所得结论的正确性.

The stability of Runge-Kutta method is studied for the second order delay differential equation. Firstly, the equation is converted to the first order differential systems by using variable substitution. Secondly, the Runge-Kutta methods are applied to the systems, and the sufficient conditions of stability of Runge-Kutta method of the first order differential systems are given, so the sufficient conditions of the second order delay differential equation are obtained. Finally, the numerical test is given to verify the conclusion.