Ordinary Differential Equations

Fabian Immler and Johannes Hölzl

26 April 2012


Session Ordinary-Differential-Equations formalizes ordinary differential equations (ODEs) and initial value problems. This work comprises proofs for local and global existence of unique solutions (Picard-Lindelöf theorem). Moreover, it contains a formalization of the (continuous or even differentiable) dependency of the flow on initial conditions as the flow of ODEs.

Not in the generated document are the following sessions:

  • HOL-ODE-Numerics: Rigorous numerical algorithms for computing enclosures of solutions based on Runge-Kutta methods and affine arithmetic. Reachability analysis with splitting and reduction at hyperplanes.
  • HOL-ODE-Examples: Applications of the numerical algorithms to concrete systems of ODEs.
  • Lorenz_C0, Lorenz_C1: Verified algorithms for checking C1-information according to Tucker's proof, computation of C0-information.

BSD License

Change history

[2014-02-13] added an implementation of the Euler method based on affine arithmetic
[2016-04-14] added flow and variational equation
[2016-08-03] numerical algorithms for reachability analysis (using second-order Runge-Kutta methods, splitting, and reduction) implemented using Lammich's framework for automatic refinement
[2017-09-20] added Poincare map and propagation of variational equation in reachability analysis, verified algorithms for C1-information and computations for C0-information of the Lorenz attractor.

Depends On

Used by


Related Entries