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
Numerical simulation of stiff systems with a diagonal splitting method
TL;DR: A linearly implicit Runge-Kutta type method is introduced that replaces the Jacobian by its diagonal blockmatrices, and using the whole Jacobian guarantees L-stability.
Journal ArticleDOI
Capillary bridge: Transition from equilibrium to hydrodynamic state
TL;DR: In this article, the authors focused on the capillary bridge behavior in the vicinity of its critical state and interpreted the information obtained from the experiment on the basis of a lubrication model.
Book ChapterDOI
Abstraction of Graph-Based Models of Bio-molecular Reaction Systems for Efficient Simulation
TL;DR: An abstraction technique to divide a graph into local structures is introduced and it is concluded that abstraction is a useful tool to analyze complex molecular reaction systems and measure their complexity.
Journal ArticleDOI
Fluid dynamics on logarithmic lattices
TL;DR: In this paper, a different approach for constructing simplified models, in which instead of simplifying equations one introduces a simplified configuration space: velocity fields are defined on multi-dimensional logarithmic lattices with proper algebraic operations and calculus, and the equations of motion retain their exact original form and naturally maintain most scaling properties, symmetries and invariants of the original systems.
Journal ArticleDOI
The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations
Oleksandr Koshkarov,Gianmarco Manzini,Gian Luca Delzanno,Cecilia Pagliantini,Vadim Roytershteyn +4 more
TL;DR: The development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations, based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions, are discussed.
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.