منابع مشابه
A note on pseudo - symplectic Runge - Kutta
In 1], the concept of pseudo-symplecticness was introduced in order to construct explicit Runge-Kutta methods which mimic symplectic ones. Of particular interest are methods of order (p; 2p),-i.e. of order p and pseudo-symplecticness order 2p-, for which the growth of the global error remains linear. The aim of this note is to show the existence of methods of orders (4; 8) and (5; 10) with a mi...
متن کاملA survey of pseudo Runge-Kutta methods
This survey collects the theoretical results in the area of pseudo RungeKutta methods (PRK ) for ordinary differential equations and it is a vehicle for a current bibliography from 1966 to 2002. PRK methods require fewer functional evaluations than Runge-Kutta methods of the same order. Byrne and Lambert (1966-1967 ) was the first who considered PRK methods in significative forms. Afterwards Co...
متن کاملRunge - 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...
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ژورنال
عنوان ژورنال: Publications of the Research Institute for Mathematical Sciences
سال: 1987
ISSN: 0034-5318
DOI: 10.2977/prims/1195176249