DISSIPATIVITY OF GENERAL LINEAR METHODS FOR DISSIPATIVE DYNAMIC SYSTEMS IN HILBERT SPACES
HILBERT空间中散逸动力系统一般线性方法的散逸稳定性

The main purpose of the present paper is to extend and unify therelevant results by Humphries & Stuart (1994), Hill (1997) and Xiao(1996) to general linear methods and dissipative dynamic systems inHilbert spaces. It is showed that, for general linear methods,dissipativity implies weak AN-stability and that, for irreduciblemethods, algebraic stability plus (L(∞))<1 impliesdissipativity.