Mathematica 12 implementation of a novel IVP discretization from a variational problem

This Mathematica script contains an implementation of the novel disretization prescription introduced in the study A. Rothkopf and J. Nordström "A new discretization technique for initial value problems based on a variational principle" arXiv:2205.14028 for the four explicit examples discussed in the manuscript. In particular it showcases how to handle the optimization task in the presence of saddle points and takes care to obtain the solution at full machine precision.