MULTISTEP NUMERICAL-METHODS FOR FUNCTIONAL-DIFFERENTIAL EQUATIONS

Different numerical methods are developed for solving retarded differe ntial equations [1,9]. Multistep numerical methods for general functio nal differential equations (FDE) were elaborated in [5,10]. In contras t to those works presented in this paper, multistep numerical methods are based on the interpolation of discrete model, but not on the appro ximation of functionals (in the right-hand side of FDE). Basic attenti on is given to investigating of convergence orders of the methods. In stable multistep numerical method of solving ordinary differential equ ations (ODE) the convergence order is defined only by approximation or der and starting procedure order. In case of FDE the order of converge nce of stable multistep numerical method depends in addition on two pa rameters: the approximation orders of interpolation and extrapolation of the numerical model pre-history. (C) 1998 IMACS/Elsevier Science B. V.