刚性方程的二阶Gear方法的注记

A NOTE ON THE SECOND ORDER GEAR'S METHOD FOR STIFF DIFFERENTIAL EQUATION

构造了一个求解刚性方程的二阶差分格式,它是隐式的,并采用简单迭代求解,对于稳定系统,迭代收敛性条件与步长无关,而对不稳定系统,迭代收敛性条件对步长却有所限制,利用这一限制性条件去克服解刚性方程的二阶Gear方法时出现的“危险性”。

A second order difference scheme for stiff system is constructed,which is implicit and is solved by the simple iterative method.The convergence condition is independent of the step of integration when the stiff system is a stable one.However,for an unstable system,convergence condition is dependent on steplength and restriction should be imposed on it.We use this restricting condition to overcome 'dangerous property 'appearing in the second order Gear's method used to solve the stiff system.At last,we give some numerical examples.