Three Mathematica supported proposals for the discretization of nonlinear dynamical control systems

In this paper, we present a library of functions in Mathematica allowing to perform some experiments on sampling and interpolation in dynamical control systems. Some of these functions implement fundamental techniques in dynamical system theory: the Euler polygon, and the Picard iteration method, while others allow to calculate approximate solutions using nonstandard algorithms exploiting the advantages of both Euler's and Picard's method. Using Taylor polynomial approximations of vector-fields may speed up the calculation of Picard iterated solutions, even though this procedure involved double approximations.