Dissipativity of Multistep Runge-Kutta Methods for Nonlinear Volterra Delay-integro-differential Equations  

作　　者：Rui QI Cheng-jian ZHANG Yu-jie ZHANG 

机构地区：[1]China1School of Science, Naval University of Engineering, Wuhan 430033, [2]School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China [3]School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

出　　处：《Acta Mathematicae Applicatae Sinica》2012年第2期225-236,共12页应用数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (No. 11171125,91130003);Natural Science Foundation of Hubei (No. 2011CDB289);Youth Foundation of Naval University of Engineering (No.HGDQNJJ10003)

摘　　要：This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of （k, l）- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finite- dimensional and infinite-dimensional dissipativity results of （k, /）-algebraically stable Runge-Kutta methods are obtained.This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of （k, l）- algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid. The finite- dimensional and infinite-dimensional dissipativity results of （k, /）-algebraically stable Runge-Kutta methods are obtained.

关 键 词：Volterra delay-integro-differential equations multistep Runge-Kutta methods dissipativity （k l）-algebraically stable 

分 类 号：O241.81[理学—计算数学] O175.6[理学—数学]