Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
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TLDR
These new formulas are suitable for the numerical integration of heat transfer problems after discretisation of these problems in the space variables, since stability considerations, occurring in such problems, would eliminate the benefits of high-orderRunge-Kutta formulas.Abstract:
Es werden neue, expliziteRunge-Kutta-Formeln vierter und niedrigerer Ordnung mitgeteilt. Diese Formeln enthalten eine Schrittweiten-Kontrolle, die auf einer vollstandigen Erfassung des ersten Gliedes des lokalen Abbruchfehlers basiert. Die Formeln haben wesentlich kleinere Abbruchfehler als entsprechende Formeln anderer Autoren. Diese neuen Formeln eignen sich zur numerischen Integration von in den Raumvariablen diskretisierten Warmeleitungsproblemen, da die bei solchen Problemen auftretenden Stabilitatsverhaltnisse die zulassige Schrittweite vonRunge-Kutta-Formeln hoherer Ordnung beeintrachtigen wurden. Die Formeln werden auf ein Beispiel fur ein Warmeleitungsproblem angewandt.read more
Citations
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Journal ArticleDOI
A force evaluation free method to N-body problems: Binary interaction approximation
TL;DR: It is shown that, although the energy conservation of the BIA scheme is worse than the 4th order Hermite integrator for similar elapsed, or the wall-clock times, the individual errors in position and in velocity are much better than HMT4.
Journal ArticleDOI
Implicit ODE solvers with good local error control for the transient analysis of Markov models
Víctor Suñé,Juan A. Carrasco +1 more
TL;DR: This paper shows that when applied to the transient analysis of CTMCs, many implicit ODE solvers are such that the linear systems involved in their steps can be solved by using iterative methods with strict control of the 1-norm of the error.
Interpolación doble de hermite y su aplicación a métodos runge-kutta
TL;DR: In this paper, a metodo numerico for resolver el problem of valor inicial is presented, haciendo uso de un metodo de extrapolacion for: and se muestra un ejemplo obtenido con la ayuda de Mathematica.
Book ChapterDOI
Computer-Based Exercises to the Lecture “Digitale Simulation”
G. Roppenecker,N. F. Benninger +1 more
TL;DR: PC-based exercises have been developed as an efficient supplement to the lecture itself on digital simulation techniques, in order to achieve a real understanding of these methods.
Journal Article
Revised Adomian Decomposition Method for the Solution of Modelling the Polution of a System of Lakes
TL;DR: In this article, the Revised Adomian decomposition method (RADM) is applied to the model of pollution for a system of three lakes interconnected by channels and three input models were solved to show that RADM can provide analytical solutions of pollution model in convergent series form.
References
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Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control
TL;DR: Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.
Journal ArticleDOI
Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
TL;DR: New explicit fifth- and seventh-orderRunge-Kutta formulas are derived that include a stepsize control procedure based on a complete coverage of the leading term of the local truncation error.