常微分方程向前步组合离散化方法

ORWARD STEP COMBINATIVE DISCRETIZATION METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS

一、一般理论 关于常微分方程组初值问题的数值求解,[1]首先提出:对方程组中各个微分方程采用不同的数值积分公式和不同的积分步长同时进行数值积分的思想.由这种思想构造的算法称为组合算法,在大系统的数字仿真等数值计算中得到了广泛的应用.国外正在发展的多速率算法或多帧速算法,是它的特例.由于并行处理机系统的迅速发展,这类算法将会得到更广泛的应用和进一步的研究.

1. A general theory In this paper we consider general aspects of forward step combinative discrettization me-thods for ordinary differential equations. A general approach to the construction for the theo-retical scheme of the methods is given. Under Some assumptions, we prove the convergence ofthe methods and give the order of the global discretization error.2. Practical methods In this paper we consider practical methods of forward step combinative discretizationmethods for ordinary differential equations. The general classes of one-step methods and li-near multistep methods are discussed. Under some assumptions which are satisfied easily, weobtain the convergence for these methods.