一类求解刚性常微分方程的半隐式多步RK方法

将线性多步方法与Ｒｏｓｅｎｂｒｏｋ和Ｈａｉｎｅｓ等提出的半隐式ＲＫ方法相结合，构造了一类求刚性常微分方程的半隐式多步ＲＫ方法。该方法具有Ａ稳定性，比普通的多步ＲＫ方法稳定性更好，同时，在求解过程中不必求解非线性方程组，大大减少了计算量，和普通的半隐式ＲＫ方法相比，该方法具有更高的阶。数值结果也表明了这类方法在求解非线性刚性常微分方程方面的优越性。

One class of semi-implicit mulltistep Runge-Kutta method for stiff ODEs

A class of semi implicit multistep Runge Kutta method is the combination of Multistep Runge Kutta method and semi implicit Runge Kutta method which solving nonlinear stiff ordinary differential equations (ODEs). Such method is A stable, more stable than Multistep Runge Kutta method. The other advantage is its little computation: in each integration step, the computation consists of s solutions of linear equation with dimension of m . Compared with semi implicit Runge Kutta method, the semi implicit Multistep Runge Kutta method has higher order. Numerical experiments showed that this method is very efficient in solving nonlinear stiff ODEs.