Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
Reads0
Chats0
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
More filters
Journal ArticleDOI
Kinetic analysis of a general model of activation of aspartic proteinase zymogens involving a reversible inhibitor. II. Contribution of the uni- and bimolecular activation routes.
A. Muñoz-Lopez,A. Sotos-Lomas,Enrique Arribas,Julio Escribano,J. Masiá-Pérez,Jose Luis Muñoz-Muñoz,Ramón Varón +6 more
TL;DR: A way to predict the time course of the relative contribution as well as the effect on this relative weight of the initial zymogen, inhibitor and activating enzyme concentrations of the uni- and bimolecular routes is suggested.
Journal ArticleDOI
Numerical strategies for the system of first-order IVPS using the RK–Butcher algorithm
TL;DR: A new method of analysis for first-order initial-value type ordinary differential equations using the Runge–Kutta (RK)–Butcher algorithm, which can be easily implemented in a digital computer and the solution can be obtained for any length of time.
Fixed Point Iteration Method
TL;DR: In this paper, the problem of finding approximate solutions of the equation x)0 f(x) is discussed and a fixed point iteration method called Newton's method is discussed.
Journal ArticleDOI
フォボス・ランデブ軌道の設計・解析
TL;DR: In this article, a new orbit for the global observation of Phobos, the first satellite of Mars, is presented, which is named as the Phobos-Rendezvous Orbit.
Journal ArticleDOI
Using a Template Engine as a Computer Algebra Tool
TL;DR: In this article, the authors propose a library and scripts for automated generation of routine functions in the Julia programming language for a set of numerical schemes of Runge-Kutta methods.
References
More filters
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.