Continuous versus discrete structures I -- Discrete embeddings and ordinary differential equations

Jacky Cresson, Frédéric Pierret

Published 2014-11-26Version 1

We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit three main discrete associate : the differential, integral or variational discrete embeddings which corresponds to classical numerical scheme including variational integrators.