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
Experiments with direct integration algorithms for ordinary differential equations in structural dynamics
Jon Braekhus,Jan Ole Aasen +1 more
TL;DR: In this article, various explicit integration methods are compared with an implicit method on two dynamic problems in solid mechanics and some effects of steplength control on the behaviour of explicit and implicit methods are pointed out and illustrated by the problems studied.
Journal ArticleDOI
Approximate methods for the fast computation of EPR and ST-EPR spectra. II. Gaussian preconvolution followed by Runge-Kutta solution of the master supe
TL;DR: In this paper, the inclusion of molecular motion, microwave radiation, and Zeeman modulation effects into the theory of EPR line-shapes results in an algebraic superm.
Journal ArticleDOI
Fully conservative spectral Galerkin–Petrov method for the inhomogeneous Boltzmann equation
Torsten Keßler,Sergej Rjasanow +1 more
TL;DR: An application of a Galerkin-Petrov method to the spatially one-dimensional Boltzmann equation is presented, which automatically insures the exact conservation of mass, momentum and energy in the three-dimensional velocity space.
Journal ArticleDOI
Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension
TL;DR: In this article, a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions is presented.
Journal ArticleDOI
Modified Runge–Kutta Verner methods for the numerical solution of initial and boundary-value problems with engineering applications
T. E. Simos,G. Papakaliatakis +1 more
TL;DR: Numerical and theoretical results in some problems of the plate deflection theory show that this new approach is more efficient compared with the well-known classical sixth order Runge–Kutta Verner method.
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.