| Home |
| About |
| Submission |
| Updating Entries |
| Using Entries |
| Search |
| Statistics |
| Index |
| Download |
Ordinary Differential Equations
| Title: | Ordinary Differential Equations |
| Authors: | Fabian Immler and Johannes Hölzl |
| Submission date: | 2012-04-26 |
| 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:
|
| 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 |
| 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},
}
|
| License: | BSD License |
| Depends on: | Affine_Arithmetic, Automatic_Refinement, Collections, Refine_Monadic, Show |
| Used by: | Differential_Dynamic_Logic |
| Status: [skipped] | This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. |
|
Proof outline Proof document |
| Browse theories |
| Download this entry |
Older releases:
|