Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
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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Predictive design of polymer molecular weight distributions in anionic polymerization
TL;DR: In this article, a detailed kinetic description of polymer initiation and propagation, including the association and dissociation equilibria of the living polymer chain ends, is presented, which can be used to prepare any desired arbitrary MWD.
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Hypernuclear no-core shell model
TL;DR: In this article, the authors extend the no-core shell model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-Λ hypernuclei.
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A fifth-order interpolant for the Dornand and Prince Runge-Kutta method
TL;DR: Some numerical experiments with the nonstiff DETEST problems show that the proposed optimal method has a good interpolatory behavior.
Journal ArticleDOI
Kinetics of promoter search by Escherichia coli RNA polymerase. Effects of monovalent and divalent cations and temperature.
P T Singer,C W Wu +1 more
TL;DR: The effect of salt concentration and temperature on the kinetics of promoter search by RPase using plasmid pAR1319 DNA, which contains the A2 early promoter from bacteriophage T7, as template is described.
Journal ArticleDOI
The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations
TL;DR: Two Rosenbrock-Wanner type methods for the numerical treatment of differential-algebraic equations are presented, one derived from the Runge-Kutta-Fehlberg 4(5)-pair, where a semi-implicit Rosen Brock- Wanner method is embedded in order to solve the nonlinear equations.
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.