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
The expression of kinetic isotope effects during the time course of enzyme-catalyzed reactions
TL;DR: The primary finding is that, if significant depletion of a second substrate occurs during the course of an enzymatic reaction, then the expression of an isotope effect will change extensively in a manner which is not anticipated by the correctional equation.
Journal ArticleDOI
Quantifying Chaos by Various Computational Methods. Part 2: Vibrations of the Bernoulli-Euler Beam Subjected to Periodic and Colored Noise
Jan Awrejcewicz,Anton V. Krysko,Anton V. Krysko,Nikolay P. Erofeev,Vitalyi Dobriyan,M. A. Barulina,Vadim A. Krysko +6 more
TL;DR: It has been shown that the introduced concept of phase transition allows for further generalization of the problem and the concept has been extended to a so-called noise-induced transition, which is a novel transition type exhibited by nonequilibrium systems embedded in a stochastic fluctuated medium.
Journal ArticleDOI
The positive column with negative ions in a magnetic field at low pressure
R N Franklin,J Snell +1 more
TL;DR: In this article, the effect of axial magnetic field on the structure of the positive column at low pressures is examined in situations where negative ions are present and where they may dominate in density over electrons.
Book ChapterDOI
The Numerical Solution of Ordinary Differential Equations: Initial Value Problems
Robert May,John Noye +1 more
TL;DR: In this article, the authors discuss the numerical solution of ordinary differential equations and describe several autonomous systems of differential equations, including the graphical method and the Taylor series methods, for finding an approximate solution to a single first-order equation.
Journal ArticleDOI
Optimal control of singular systems using the rk–butcher algorithm
TL;DR: The obtained discrete solutions using the RK–Butcher algorithms are compared with the exact solutions of the optimal control problem and are found to be very accurate.
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.