一类二级隐式Runge-Kutta方法的非线性稳定性及B-收敛性

NONLINEAR STABLLITY AND B-CONVERGENCE FOR A CLASS OF TWO-STAGE IMPLICIT RUNGE-KUTTA METHODS

本文给出了一类二级全隐式的 Runge-Kutta(R-K)方法,讨论了它的非线性稳定性及 B-收敛性,最后将这类方法与传统的二级 R-K 方法作了比较,结果表明我们的方法不仅对非 stiff 问题较为适用(有较高的传统阶)而且也同样适用于 stiff 问题(有完全相当的最优 B-收敛阶)

This paper presents a class of two-stage completely implicit Runge-Kutta methods and discusses its nonlinear stability and B-convergence.Finally,a comparision between the methods and some classical two-stage R-K methods is given,the results indicate that our methods is applicable to both nonstiff systems and stiff systems