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A modified version of explicit Runge-Kutta methods for energy-preserving

Guang-Da Hu (2014)


In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments...

Comparing numerical integration schemes for a car-following model with real-world data

Přikryl, Jan, Vaniš, Miroslav (2017)

Programs and Algorithms of Numerical Mathematics

A key element of microscopic traffic flow simulation is the so-called car-following model, describing the way in which a typical driver interacts with other vehicles on the road. This model is typically continuous and traffic micro-simulator updates its vehicle positions by a numerical integration scheme. While increasing the order of the scheme should lead to more accurate results, most micro-simulators employ the simplest Euler rule. In our contribution, inspired by [1], we will provide some additional...

Erweiterung des G -Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.

Reiner Vanselow (1983)

Aplikace matematiky

In der vorliegenden Arbeit wird der G -Stabilitätsbegriff von Dahlquist, der die Grundlage für Stabilitätsuntersuchungen bei linearen Mehrschrittverfahren zur Lösung nichtlinearet Anfangswertaufgaben bildet, auf die Klasse der linearen Mehrschrittblockverfahren übertragen. Es wird nachgewiesen, das Blockverfahren, die in diesem Sinne stabil sind, höchstens die Konsistenzordnung 2 haben können.

Explizite Konstruktion von linearen Mehrschrittblockverfahren

Reiner Vanselow (1983)

Aplikace matematiky

In der vorliegenden Arbeit wird für lineare Mehrschrittblock verfahren zur numerischen Lösung von Anfangswertaufgaben eine explizite Konstruktionsmöglichkeit angegeben. Sie ermöglicht es, zu einem gegebenen Stabilitätspolynom ohne Lösung eines linearen Gleichungssystems die Koefizienten des zugehörigen Blockverfahrens zu berechnen.

Generalized periodic overimplicit multistep methods (GPOM methods)

Hassan Nasr Ahmed Ismail (1979)

Aplikace matematiky

The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.

On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D⋆⋆

G. Berkolaiko, A. Comech (2012)

Mathematical Modelling of Natural Phenomena

We study the spectral stability of solitary wave solutions to the nonlinear Dirac equation in one dimension. We focus on the Dirac equation with cubic nonlinearity, known as the Soler model in (1+1) dimensions and also as the massive Gross-Neveu model. Presented numerical computations of the spectrum of linearization at a solitary wave show that the solitary waves are spectrally stable. We corroborate our results by finding explicit expressions for...

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