Abstract. The algorithms of constructing optimal functional estimates and guaranteed estimates of nonstationary parameters of differential equations are proposed. The results are generalized to discrete-time models. These algorithms can be used to predict the dynamics of systems of differential equations. The results of a numerical experiment for the problem of constructing guaranteed estimates for the mathematical model of propagation of one type of information are considered.

Keywords: differential equations, nonstationary parameters, optimal functional estimation, guaranteed estimation, uncertainty.