Une formule de Runge-Kutta

Méthodes de Runge-Kutta-Fehlberg

Une courte démonstration de la formule de Campbell-Hausdorff

We give a simple proof of an algorithm for computing the terms of the Campbell-Hausdorff formula. 2000 AMS Subject Classification: Primary: 22E15; Secondary: 22E60 Soient G un groupe de Lie et g = T1G son algèbre de Lie, vue comme l’espace tangent à G en l’élément neutre 1. Alors il existe un voisinage V de 0 dans g et un voisinage U de 1 dans G tels que la restriction de l’application exponent...

Une formule analytique pour les polynômes de Macdonald

We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtained by inverting the Pieri formula. Résumé Nous donnons le développement analytique explicite de tout polynôme de Jack ou de Macdonald sur les fonctions symétriques élémentaires (resp. complètes modifiées). Nous obten...

Runge - Kutta Methods page RK 1 Runge - Kutta Methods

Literature For a great deal of information on Runge-Kutta methods consult J.C. Butcher, Numerical Methods for Ordinary Differential Equations, second edition, Wiley and Sons, 2008, ISBN 9780470723357. That book also has a good introduction to linear multistep methods. In these notes we refer to this books simply as Butcher. The notes were written independently of the book which accounts for som...

Accelerated Runge-Kutta Methods

Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size Accerelated-Runge-Kutta methods that ...