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
Application of series method with Padé and Laplace-Padé resummation methods to solve a model for the evolution of smoking habit in Spain
TL;DR: In this paper, the authors obtained approximated analytical solutions of a mathematical model of the evolution of smoking habit in Spain using the series method using the Pade and Laplace-Pade resummation methods.
Journal ArticleDOI
A program for the numerical integration of enzyme kinetic equations using small computers.
Rafael Franco,Enrique I. Canela +1 more
TL;DR: A simple program to integrate differential equations is given that has been used to integrate the differential equations corresponding to a single reaction- single enzyme, a bireaction-single enzyme and a four reaction-four substrate-single enzymes mechanism.
Journal ArticleDOI
Solving ordinary differential equations for simulation
TL;DR: Runge-Kutta formulas are given which are methods permitting interpolation which use overlap into the succeeding step to reduce the cost of a step and its error estimate.
Journal ArticleDOI
Kinetics of autocatalytic zymogen activation measured by a coupled reaction: pepsinogen autoactivation.
TL;DR: A dimensionless distribution coefficient was defined, which shows mathematically whether the intra- or the intermolecular route prevails once the kinetic parameters involved in the system are known, and Experimental design and kinetic data analysis procedures to evaluate the kinetic Parameters are suggested.
Journal ArticleDOI
On the contact interaction of a two-layer beam structure with clearance described by kinematic models of the first, second and third order approximation
V.A. Krysko,Jan Awrejcewicz,O. A. Saltykova,O. A. Saltykova,Irina V Papkova,Anton V. Krysko,Anton V. Krysko +6 more
TL;DR: In this article, the contact interaction of two geometrically non-linear beams with a small clearance is studied by employing various approximations of the kinematic beam models, and the results of convergence versus the number of partition points along the spatial co-ordinate and time steps are investigated.
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.