HILBERT空间中散逸动力系统一般线性方法的散逸稳定性  

DISSIPATIVITY OF GENERAL LINEAR METHODS FOR DISSIPATIVE DYNAMIC SYSTEMS IN HILBERT SPACES

作　　者：肖爱国[1] 

机构地区：[1]湘潭大学数学系

出　　处：《计算数学》2000年第4期429-436,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金!(No.19871070);中国科学院数学与系统科学院创新基金!(No.A757D9I0)资助项目.

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

关 键 词：一般线性方法 散逸稳定性 散逸动力系统 HILBERT空间 数值解 

分 类 号：O241[理学—计算数学]