Multistep numerical methods for functional differential equations

Different numerical methods are developed for solving retarded differential equations [1,9]. Multistep numerical methods for general functional differential equations (FDE) were elaborated in [5,10]. In contrast to those works presented in this paper, multistep numerical methods are based on the interpolation of discrete model, but not on the approximation of functionals (in the right-hand side of FDE). Basic attention is given to investigating of convergence orders of the methods. In stable multistep numerical method of solving ordinary differential equations (ODE) the convergence order is defined only by approximation order and starting procedure order. In case of FDE the order of convergence of stable multistep numerical method depends in addition on two parameters: the approximation orders of interpolation and extrapolation of the numerical model pre-history. (C) 1998 IMACS/Elsevier Science B.V.