Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
Reads0
Chats0
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
More filters
Journal ArticleDOI
Low frequency acoustic and electromagnetic scattering
S. I. Hariharan,R C MacCamy +1 more
TL;DR: In this article, two classes of problems arising from acoustics and electromagnetics scattering in the low frequency stations are dealt with: the first class is solving Helmholtz equation with Dirichlet boundary conditions on an arbitrary two dimensional body while the second one is an interior-exterior interface problem with the same equation in the exterior.
Book ChapterDOI
Numerical solutions of initial value problems for ordinary differential equations
TL;DR: A survey of the current situation regarding programs for solving initial value problems associated with ordinary differential equations, and conclusions and recommendations about what methods to use on non-stiff problems are presented.
Journal ArticleDOI
Symplectic phase flow approximation for the numerical integration of canonical systems
S. Miesbach,Hans Josef Pesch +1 more
TL;DR: In this article, a Runge-Kutta-type ansatz for the generating function is proposed to realize the integration steps by canonical transformations, which preserve the Poincare invariants and mimic relevant qualitative properties of the exact solutions.
Journal ArticleDOI
Solar p-mode damping rates: Insight from a 3D hydrodynamical simulation
TL;DR: In this article, a 3D hydrodynamical simulation of a solar high-spatial resolution and long-duration 3D simulation computed with the ANTARES code is used to investigate the coupling between turbulent convection and the normal modes of the simulated box.
Dissertation
The closest point method for time-dependent processes on surfaces
TL;DR: This thesis concerns the numerical solution of time-dependent partial differential equations (PDEs) on general surfaces using a recent technique known as the Closest Point Method, which represents surfaces with a closest point representation which leads to great flexibility with respect to surface geometry, among other advantages.
References
More filters
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.