求解Stiff常微分方程组的一类二阶导数多项式配置法

A CLASS OF POLYNOMIAL COLLOCATION METHODS WITH SECOND DERIVATIVE FOR SOLVING STIFF ORDINARY DIFFERENTIAL EQUATIONS

本文利用多项式配置的思想构造了一类带有二阶导数的配置法。此类方法具有单步法的形式,其每步联立得到m个点上的数值解。文中证明了此类方法的收敛阶为2m+1。对于等间距置点的情形,3、5、7和9阶公式均是A(α)-稳定的,相应最大α为90°.89°50′,88°22′和85°16′。从计算上考虑,此类方法尤其适于求解自治Stiff常微分方程。

In this paper, a class of polynomial collocation methods with the second deriva live is derived for efficient integration of stiff systems. The methods are of one^step type, and the numerical solutions at m-point can simultaneously be obtained for each application of the formulas. It is shown that this class of methods is of order 2m+1 and the stability is analysed.