非线性中立型延迟微分方程稳定性分析

This paper is devoted to the stability analysis of both the true solution and the numerical approximations for nonlinear systems of neutral delay differential equations(NDDEs) of the general form y′(t)=F(t，y(t)，G(t，y(t-τ-(t))，y′(t-τ-(t)))). We first present a sufficient condition on the stability and asymptotic stability of theoretical solution for the nonlinear systems. This work extends the results recently obtained by A.Bellen et al. for the form y′(t)=F(t，y(t)，G(t，y(t-τ-(t))，y′(t-τ-(t)))). Then numerical stability of Runge-Kutta methods for the systems of neutral delay differential equations is also investigated. Several numerical tests listed at the end of this paper to confirm the above theoretical results.

STABILITY ANALYSIS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

This paper is devoted to the stability analysis of both the true solution and the numerical approximations for nonlinear systems of neutral delay differential equa-tions(NDDEs) of the general form y'(t) = F(t, y(t), y(t-r(t)), y'(t-r(t))). We first present a sufficient condition on the stability and asymptotic stability of theoretical solution for the nonlinear systems. This work extends the results recently obtained by A.Bellen et al. for the form y'(t) = F(t,y(t),G(t,y(t-T(t)),y'(t-T(t)))). Then numerical stability of Runge-Kutta methods for the systems of neutral delay differential equations is also investigated. Several numerical tests listed at the end of this paper to confirm the above theoretical results.