二级对角隐Runge-Kutta方法的B-收敛性

B-CONVERGENCE OF THE TWO-STAGE DIAGONALLY IMPLICIT R-K METHODS

本文讨论了二级对角隐 Runge-Kutta 方法的 B-相容,B-稳定及 B-收敛性,导出了方法的1阶最优 B-收敛性,从而改进和推广了朱方生1988年的结果.本文讨论 B-相容,B-稳定性所用方法不同于 Dekker & Verwer 1984年的方法,所得误差估计较前更为精确,其中 B-稳定性的讨论也推广和修正了 Burrage & Butcher 1979年的结果.

This paper explores B-consistency,B-stability and B-convergence of the two-stage diagonally implicit R-K methods,and the results improve and generalize those of Zhu Fangsheng(J.of Math.,PRC,1988).The technique used for discussions of the B-stability and B-consistency in this paper is different from that of Dekker & Verwer in 1984,the error bounds obained are sharper than those derived by them.The result about B-stability also generalizes and corrects that of Burrage & Butcher in 1979.