Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation - Archive ouverte HAL Access content directly
Journal Articles Optimization Methods and Software Year : 2018

Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation

Abstract

A novel approach to bound the local truncation error of explicit and implicit Runge-Kutta methods is presented. This approach takes its roots in the modern theory of Runge-Kutta methods, namely the order condition theorem, defined by John Butcher in the 60's. More precisely, our work is an instance, for Runge-Kutta methods, of the generic algorithm defined by Ferenc Bartha and Hans Munthe-Kaas in 2014 which computes B-series with automatic differentiation techniques. In particular, this specialised algorithm is combined with interval analysis tools to define validated numerical integration methods based on Runge-Kutta methods.
Fichier principal
Vignette du fichier
articleAD16-hal.pdf (603.28 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01498372 , version 1 (29-03-2017)

Identifiers

Cite

Olivier Mullier, Alexandre Chapoutot, Julien Alexandre Dit Sandretto. Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation. Optimization Methods and Software, 2018, ⟨10.1080/10556788.2018.1459620⟩. ⟨hal-01498372⟩
228 View
1111 Download

Altmetric

Share

Gmail Facebook X LinkedIn More