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
Partitioned Runge-Kutta methods with stiffness detection and stepsize control
TL;DR: An automatic stiffness detection and a stepsize control for two different algorithms are developed and usually RKF4RW is the faster algorithm and the system stiffness detection works more reliable than the componentwise stiffness detection in PRK4.
Journal ArticleDOI
Klassische Runge-Kutta-Nyström-Formeln mit Schrittweiten-Kontrolle für Differentialgleichungen $$\ddot x = f(t,x,\dot x)$$@@@Classical Runge-Kutta-Nyström formulas with stepsize control for differential equations $$\ddot x = f(t,x,\dot x)$$
Journal ArticleDOI
Chemical preparation of ultra-fine aluminium oxide by electric arc plasma
TL;DR: In this paper, it has been proved that the rate determining step of the process is the evaporation of the aluminium powder and that the most appropriate thermodynamic and kinetic conditions for obtaining pure, finely dispersed product has been determined.
Journal ArticleDOI
Mathematical modeling and sensitivity analysis of G1/S phase in the cell cycle including the DNA-damage signal transduction pathway.
TL;DR: A novel mathematical model is constructed which integrated G1/S-checkpoint model with a signal transduction of DNA damage model and performed some numerical simulations which suggested that proposed model is biologically appropriate.
Journal ArticleDOI
Efficient path tracking methods
TL;DR: The effects of the choice of predictor method on the performance of a tracker is analyzed, and details for using Runge-Kutta methods in conjunction with adaptive precision are provided.
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.