منابع مشابه
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...
متن کاملAccelerated 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 ...
متن کاملOptimum Runge-Kutta Methods
The optimum Runge-Kutta method of a particular order is the one whose truncation error is a minimum. Various measures of the size of the truncation error are considered. The optimum method is practically independent of the measure being used. Moreover, among methods of the same order which one might consider using the difference in size of the estimated error is not more than a factor of 2 or 3...
متن کاملDiagonally Implicit Symplectic Runge-Kutta Methods with Special Properties
The numerical integration of Hamiltonian systems is considered in this paper. Diagonally implicit Symplectic Runge-Kutta methods with special properties are presented. The methods developed have six and seven stages algebraic order up to 5th and dispersion order up to 8th.
متن کاملSymmetries of Runge-Kutta methods
A new (abstract algebraic) approach to the solution of the order conditions for Runge-Kutta methods (RK) and to the corresponding simplifying assumptions was suggested in [9, 10]. The approach implied natural classification of the simplifying assumptions and allowed to find new RK methods of high orders. Here we further this approach. The new approach is based on the upper and lower Butcher’s a...
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2013
ISSN: 1742-6596
DOI: 10.1088/1742-6596/413/1/012033