Reseña: The Picard algorithm for ordinary differential equations in Coq
Se ha publicado un artículo de razonamiento formalizado en Coq sobre ecuaciones diferenciales titulado The Picard algorithm for ordinary differential equations in Coq.
Sus autores son Evgeny Makarov and Bas Spitters (de la Universidad de Nimega, Países Bajos).
Su resumen es
Ordinary Differential Equations (ODEs) are ubiquitous in physical applications of mathematics. The Picard-Lindelöf theorem is the first fundamental theorem in the theory of ODEs. It allows one to solve differential equations numerically. We provide a constructive development of the Picard-Lindelöf theorem which includes a program together with sufficient conditions for its correctness. The proof/program is written in the Coq proof assistant and uses the implementation of efficient real numbers from the CoRN library and the MathClasses library. Our proof makes heavy use of operators and functionals, functions on spaces of functions. This is faithful to the usual mathematical description, but a novel level of abstraction for certified exact real computation.
Las teorías desarrolladas se encuentran aquí.