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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Non-linear sphere tracing for rendering deformed signed distance fields
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The geodesic motion of S2 and G2 as a test of the fermionic dark matter nature of our galactic core.
TL;DR: In this paper, it was shown that the Ruffini-Arguelles-Rueda (RAR) model can explain the S2 and G2 motion with respect to the core-halo fermionic dark matter (DM) profile.
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Numerical solution of an industrial robot arm control problem using the RK Butcher algorithm
TL;DR: The exact solution of the system of equations representing the arm model of a robot have been compared with the corresponding discrete solutions at different time intervals using the RK Butcher algorithm and also the absolute error between the exact and discrete solutions have been determined.
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Geometric pinning and antimixing in scaffolded lipid vesicles.
TL;DR: In this paper, a combination of experiments on lipid vesicles supported by colloidal scaffolds and theoretical work was demonstrated that the local geometry and global chemical composition of the bilayer determine both the spatial arrangement and the amount of mixing of the lipids.
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Kinetics of intra- and intermolecular zymogen activation with formation of an enzyme-zymogen complex.
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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.