关于MBDF方法的分裂线性多步法

On the Split MBDF Multistep Methods

本文对一类修正的BDF方法利用分裂法思想得到一组具有隐式预报式的预报——校正法.由于预报及校正公式皆为隐式法,所以该预报——校正对具有极好的绝对稳定性.同时因为预报与校正公式出自同一多步法而使得它们的Jacobi迭代矩阵同为??这样方法的计算量并没有很大的增加.本文对我们所给的分裂线性组步法与其它一些线性多步法作了比较,表明我们所给方法的数值稳定性远优于其它一些方法,最后给出的数值例子也证明了这一点.

This paper presents a class of precdictor-corrector methods with implicit predictors by applying the concept of split to the MBDF methods.These predictor-corrector methods have excellent absolute stabilities Since both the predictors and correctors are implicit.Meanwhile, since the predictors and correctors derive from the Same multistep methods, both of them have the same Jacobi matrices(α_kI-(1-θ)h??f(x,y)/??y), which implies that no large additional amount of computational effort is needed.This paper also gives comparisons of our methods with some other multistep methods.Numerical examples show that for some problems the methods in this paper are more suitable than others.