Abstract: |
Session HOL-ODE 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-Refinement:
Intermediate session combining \texttt{HOL-ODE} and Lammich's (automatic) refinement framework.
- 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 (e.g., van der Pol and Lorenz
attractor).
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BibTeX: |
@article{Ordinary_Differential_Equations-AFP,
author = {Fabian Immler and Johannes Hölzl},
title = {Ordinary Differential Equations},
journal = {Archive of Formal Proofs},
month = apr,
year = 2012,
note = {\url{http://isa-afp.org/entries/Ordinary_Differential_Equations.shtml},
Formal proof development},
ISSN = {2150-914x},
}
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