用加权平均方法构造新的隐式线性多步法公式

CONSTRUCTION OF THE NEW IMPLICT LINEAR MULTISTEP METHODS FORMULAS BASED ON WEIGHTED AVERAGE METHODS

在已知的线性多步法公式中,用两个较适合的线性多步法进行加权平均就能构造出一系列新的隐式线性多步法公式,而且其中有些公式可能具有较好的性质,如稳定域增大.从而使得解刚性方程时,可以根据对稳定域与截断误差不同的需求来选择公式,以达到在适合的稳定域下,截断误差最小.经过数值试验验证,本文举出的实例中用加权平均方法构造出的有些新公式的稳定域大于原来两个公式任一个的稳定域,可应用于求解常微分方程初值问题的刚性问题.

With two known linear multistep methods formulas, a series of the new implicit linear multistep methods can be constructed by weighted average method. Some of them may have better formulae nature, such as large stable regions. Therefore, some linear multistep formulae can be selected for different demands of stable region and error of truncation to get the minimum error of truncation in suitable stable region. In this paper, some of new formulae we constructed, have more large stable regions than any of the original formulae, are valid for the initial-value problem of the stiff problem in ordinary differential equations.