Dissipativity Analysis Of The Numerical Methods For A Class Of Nonlinear Neutral Volterra Delay-Integro-Differential Equations

Let X be a real or complex Hilbert space with the inner product<·,·)and the correspond-ing norm || · ||.Consider the nonlinear neutral delay-integro-differential equations(NDIDEs)where ?>0 is given constants.f and K are given continuous mappings and satisfy the following conditions:Re(f(t,y,u,v),y>??+?||y||2+?1||/(t,0,u,v)||2,t?0,y,u,v?X,||f{t,y,u,v)||2 ? Ly||y||2 + ?2||f(t,0,u,v)||2,t ? 0,y,u,vE X,||f(t,0,u,v)||2 ? Lu||u||2+Lv||2||,t? 0,u,v E X,||K(t,s,u,v)|| ? ?||u|| +Lk||v||,(t,s)? D,u,v ? X,where D = {(t,s):t ?[0,+?),s?[t-?,t },?,?,?1,?2,?,Ly,Lu,Lvare constants.In this paper,by using Halanary inequality,the sufficient conditions are given which ensures this class system itself to be disspative.The dissipativity of one-leg methods and Runge-Kutta methods for solving this class problems are studied and the sufficient conditions which inhere the dissipativity of system itself are given.Finally,some numerical experiments are present,the results further verify the theoretical results.