Dissipativity Analysis Of General Linear Methods For Coupled System Of Nonlinear Functional Differential And Functional Equations

Let X be a real(or complex)Hilbert space,<·,·>and ?·? are the inner product in X and the corresponding inner product norm respectively,Consider the initial value problem of a class of nonlinear functional differential and functional equations in X as follows where ?? 0 are given constant delay,?,? are given continuous function,satisfying the consistency condition:?(0)=g(0,?(0),?(-?),?(-?)).Mapping f:[0,+?)×X × X × X?X and g:[0,+?)×X × X × X?X continuous function,and for all t?0,y,u,v,w?X,f and g satisfy:Re(f(t,u,v,w),u>??1+??u?2+,?1?v?2+?2?w?2,?g(t,u,v,w)?2??2+u ?u?2+Lv?v?2+Lw?w?2,here coefficient are ?1,?2,?1,?2,Lu,Lv,Lw are non-negative real constands,?? 0.The main results in this paper are as follows:First,when[?+?1+?2(Lv+Lu)/1-Lw]h?p/2,(k,p,0)-algebraically stable general linear meth-ods can inherit the dissipativity of the system.Secend,numerical experiment with 2 stages 2 steps multistep Runge-Kutta meth-ods have been carried out and the results also prove the correctness of the theoretical analysis.