Validated Explicit and Implicit Runge-Kutta Methods - ENSTA Paris - École nationale supérieure de techniques avancées Paris Access content directly
Conference Papers Year :

Validated Explicit and Implicit Runge-Kutta Methods

Abstract

The guaranteed solution of initial value problem of ordinary differential equations is well studied from interval analysis community. In the most of the cases Taylor models are used in this context. In contrast, in numerical analysis community other numerical integration methods, e.g., Runge-Kutta methods, are used. Indeed, these methods have very good stability properties and they can be applied on a wide variety of problems. We propose a new method to validate the solution of initial value problem of ordinary differential equations based on Runge-Kutta methods. The strength of our contribution is to adapt any explicit and implicit Runge-Kutta methods to make them guaranteed. We experimentally verify our approach against Vericomp benchmark.
Fichier principal
Vignette du fichier
chapoutot_et_al_grk.pdf (188.19 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01111240 , version 1 (29-01-2015)
hal-01111240 , version 2 (11-02-2015)

Identifiers

  • HAL Id : hal-01111240 , version 2

Cite

Alexandre Chapoutot, Julien Alexandre Dit Sandretto, Olivier Mullier. Validated Explicit and Implicit Runge-Kutta Methods. Small Workshop on Interval Methods, Jun 2015, Prague, Czech Republic. ⟨hal-01111240v2⟩
133 View
127 Download

Share

Gmail Facebook Twitter LinkedIn More