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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Journal ArticleDOI
Ion Acceleration in Arc Jet Plasma Along Open Field Lines
TL;DR: In this article, a quasi-1-D flow model is proposed to describe the ion acceleration and it is concluded that the helium ions are accelerated both by the electric field and by the increasing cross-sectional area of the supersonic flowing channel, which is determined by the magnetic flux conservation.
Journal ArticleDOI
Coupled Eulerian‐Lagrangian simulation of the penetration and braking behaviour of ship anchors in clay
Jürgen Grabe,Lingyue Wu +1 more
TL;DR: In this paper, numerical simulations of the penetration and braking behavior of ship anchors in a clay-ey seabed were presented. But the authors did not consider the impact of anchor size, soil strength and dragging speed on the penetration depth.
Journal ArticleDOI
Runge–Kutta Pairs of Orders 5(4) Trained to Best Address Keplerian Type Orbits
Vladislav N. Kovalnogov,Ruslan V. Fedorov,Tamara V. Karpukhina,T. E. Simos,Charalampos Tsitouras +4 more
TL;DR: In this article, the derivation of Runge-Kutta pairs of orders five and four that effectively uses six stages per step is considered and the coefficients provided by such a method are 27 and have to satisfy a system of 25 nonlinear equations.
Journal ArticleDOI
Rate-equation modelling and ensemble approach to extraction of parameters for viral infection-induced cell apoptosis and necrosis
TL;DR: A theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis (direct cell death).
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.