Continuous versus discrete structures I -- Discrete embeddings and ordinary differential equations
Numerical Analysis
2014-11-27 v1 Category Theory
Abstract
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.
Cite
@article{arxiv.1411.7117,
title = {Continuous versus discrete structures I -- Discrete embeddings and ordinary differential equations},
author = {Jacky Cresson and Frédéric Pierret},
journal= {arXiv preprint arXiv:1411.7117},
year = {2014}
}