Numerical stability of nonlinear delay differential equations of neutral type

This paper is devoted to the stability analysis of both the true solutions and the numerical approximations for nonlinear systems of neutral delay differential equations (NDDEs) of the form y′(t)=F(t,y(t),G(t,y(t−τ(t)),y′(t−τ(t)))). This work extends the results recently obtained by the authors Bellen et al. (BIT 39 (1999) 1–24) for the linear case. This is accomplished by considering a suitable reformulation of the given system, which transforms it into a nonlinear differential system coupled with an algebraic functional recursion. Numerical processes preserving the qualitative properties of the solutions are also investigated.