关于求解Stiff常微分方程的数值方法

我们要求方法(2)满足如下三个条件:(i)当μ→-∞时,方法(2)是绝对稳定的;(ii)在μ平面的原点邻城内有合理的稳定性质(即在Stiff稳定的定义中,值θ不能太小);(iii)选取系数α_i(i=0,1,…,k),β_(k-2),β_(k-1),β_k,使得k步方法(2)达到k阶Stiff稳定,并且具有较大的绝对稳定域。 与方法(2)相关的算子为

ON THE NUMERICAL METHOD FOR SOLVING STIFF ORDINARY DIFFERENTIAL EQUATIONS

C. W. Gear deduced stiffly stable methods of orders 1 to 6~1] based on the differen-tial method to solve stiff ordinary differential equations. In this paper a class of stifflystable LMMs of orders 1 to 7 is given. Under the assumption of the same accuracy, ithas larger absolute stability region than that of Gear's method and thus is suitable forsolving initial value problems of stiff ordinary differential equations.