求解常微分方程组的并行θ-块预估-校正法

PARALLEL θ-BLOCK PREDICTOR - CORRECTOR METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS

为并行求解常微分方程组,本文给出了一类带有参数θ的块预估-校正法,并讨论了该类方法的稳定性和校正过程的收敛性。理论分析证明,该方法不仅稳定区间比一般的块预估-校正法大许多,而且具有很大的收敛区域。因此,非常适于并行求解常微分方程初值问题。数值实验验证了这一结论。

This paper gives a class of parallel block predictor-corrector methods with a parameter θ for solving initial value problems in ordinary differential equations. The stability and convergence on iterative processes are discussed. It is proven that the methods not only have large stability intervals but also have large convergent regions, thus they are very suitable for par allel integration of ordinary differential equations.