非线性中立型延迟积分微分方程Runge-Kutta方法和线性多步法的散逸性.pdfVIP

 d t  [y(t) − Ny(t − τ )] = f(y(t),y(t − τ ), g(t,ξ,y(ξ))dξ), t ≥ 0, dt 1 1 t−τ2 y(t) = φ(t), −τ ≤ t ≤ 0, . τ , τ , τ = max{τ ,τ }, N ∈ Cd×d 1 2 1 2 d d d d d N 1, φ : [−τ, 0] → C Æ, f : C × C × C → C d d Lipschitz g : [0,+∞) × [−τ ,+∞) × C → C f g 2 : 2 2 2 d Reu − Nv,f(u,v,w) ≤ γ + αu + βv + ωw , ∀u,v,w ∈ C , d g(t,θ,s) ≤ cs, ∀t ≥ 0,t − τ ≤ θ ≤ t,s ∈ C . 2 d Æ γ,α,β,ω,c β ≥ 0,γ ≥ 0,ω ≥ 0, , C . 1) ℄ Runge-Kutta . 2) Runge-Kutta . 3) . . : Runge-Kutta . I Abstract This paper is concerned with the dissiptivity of numerical methods for non- linear neutral delay integro-differential equations  d t  [y(t) − Ny(t − τ )] = f(y(t),y(t − τ ), g(t,ξ,y(ξ))dξ), t ≥ 0, dt 1 1 t−τ2 y(t) = φ(t), −τ ≤ t ≤ 0, Where τ ,τ are positive constants and τ = max{τ ,τ }, N ∈ Cd×d is a constant 1 2 1 2 d d d matrix satisfing N 1, φ : [−τ, 0] → C is a continuous function, f : C ×C × d d