积分微分方程多步Runge-Kutta方法的散逸性  

Dissipativity of Multistep Runge-Kutta Methods for Integro-Differential Equations

作　　者：蔡白光[1] 甘四清[2] 

机构地区：[1]海南大学信息科学技术学院,海口570228 [2]中南大学数学与计算科学学院,长沙410075

出　　处：《西南大学学报（自然科学版）》2013年第5期61-67,共7页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161017);海南省自然科学基金资助项目(110002);海南省教育厅基金资助项目(Hjkj2813-09)

摘　　要：研究一类积分微分方程多步Runge-Kutta方法的散逸性.利用复合求积公式逼近积分项,当k≤1时,证明了(k,l)-代数稳定的、不可约的多步Runge-Kutta方法的有限维散逸性.此外,当k<1时,得到了该方法的无限维散逸性结果.这些结果表明所考虑的数值方法很好地继承了系统本身所具有的散逸性,丰富了数值求解这一类积分微分方程的方法.This paper is concerned with the dissipativity of multistep Runge-Kutta methods for one kind of integro-differential equations. When the integration term is approximated by the compound quadrature for- mula, it is proved that a （k,/）-algebraically stable, irreducible multistep Runge-Kutta method is dissipa- tive for finite-dimentional dynamical systems when kl. In addition, we obtain dissipativity results of this method for infinite-dimentional dynamical systems when t〈1. The results show that the multistep Runge- Kutta methods inherit the important property of the underlying systems, and enrich the numerical meth- ods for us to solve the underlying systems.

关 键 词：多步RUNGE-KUTTA方法 复合求积公式 散逸性 

分 类 号：O241.83[理学—计算数学]