【摘要】：設(shè)Cd為d維的復(fù)歐幾里得空間,·,·為其中的內(nèi)積,|| · ||是由該內(nèi)積導(dǎo)出的范數(shù).考慮如下形式的非線性泛函積分微分方程(FIDEs)初值問(wèn)題這里τ0是實(shí)常數(shù),f : [t0,+∞) × Cd × Cd→Cd,p : D × Cd→Cd,φ:[t0- τ,t0]→Cd是給定的連續(xù)映射,且f和g滿足條件Ref(t, u,v),u-w γ + α||u ||2+β|| v ||2 +η || w ||2, t t0, u,v,w ∈Cd,和|| g(t,ζ,u) || λ || u ||,e D,u ∈Cd,這里γ, α, β,η,γ是實(shí)常數(shù)且γ, -α, η非負(fù),λ0且2λ2τ2 1,D = {(t,ζ ∈ [t0,+∞),ζ∈ [t-τ,t}.本文將滿足上述條件的問(wèn)題類記作R(γ, α, β,η,λ),并研究該類問(wèn)題本身及求解該類問(wèn)題的數(shù)值方法的散逸性,獲得了如下結(jié)果.一、給出了該類問(wèn)題本身散逸的充分條件.二、得到了當(dāng)g(α +β+ +ηυ2A2) p-(1 + υ2A2)時(shí),G(c,p,0)-代數(shù)穩(wěn)定單支方法求解該類問(wèn)題是散逸的,以及當(dāng)α +β+ ηυ2λ2 0時(shí),Runge-Kutta方法求解該類問(wèn)題是散逸的.三、以G(c,p,0)-代數(shù)穩(wěn)定單支方法和Runge-Kutta方法為例進(jìn)行了數(shù)值試驗(yàn),數(shù)值計(jì)算結(jié)果與理論結(jié)果一致,從而驗(yàn)證了理論結(jié)果的正確性.
[Abstract]:Let CD be a complex Euclidean space with d dimension and the inner product of CD be the norm derived from the inner product. In this paper, we consider the (FIDEs) initial value problem of nonlinear functional differential equations in the following form, where 蟿 0 is a real constant f: [t 0, 鈭，

本文編號(hào)：2175227