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The Picard Algorithm for Ordinary Differential Equations in Coq

  • Evgeny Makarov
  • Bas Spitters
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7998)

Abstract

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.

Keywords

Coq Exact real computation Ordinary Differential Equations Constructive mathematics Type classes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Evgeny Makarov
    • 1
  • Bas Spitters
    • 1
  1. 1.Radboud University NijmegenThe Netherlands

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