Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. I. Motion of a Single Particle.
Energy Conserving, Arbitrary Order Numerical Solutions of the N-Body Problem.
Epsilon-inflation with contractive interval functions
For contractive interval functions we show that results from the iterative process after finitely many iterations if one uses the epsilon-inflated vector as input for instead of the original output vector . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.
Equilibria of Runge-Kutta methods.
Erratum: On the convergence of multistep methods for nonlinear stiff differential equations.
Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics
In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for exponential operator splitting methods of (nonstiff) order p applied to the multi-configuration time-dependent...
Error analysis of QR algorithms for computing Lyapunov exponents.
Error Bounds for Numerical Solutions of Ordinary Differential Equations.
Error estimates and step-size control for the approximate solution of a first order evolution equation
Error estimates of a numerical method for a class of nonlinear evolution equations
Erweiterung des -Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.
In der vorliegenden Arbeit wird der -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.
Estimation of longest stability interval for a kind of explicit linear multistep methods.
Étude numérique des solutions périodiques d'une équation du second ordre
Euler-Verfahren für neutrale Funktional-Differentialgleichungen.
Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals.
Explicit Runge-Kutta Formulas with Increased Stability Boundaries.
Explicit two-step Runge-Kutta methods
The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order the minimal number of stages for explicit TSRK method of order is equal to the minimal number of stages for explicit Runge-Kutta method of order . Numerical results are presented which...
Explizite Konstruktion von linearen Mehrschrittblockverfahren
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.
Exponential Multistep Methods for Ordinary Differential Equations
Extensions of the HHT- method to differential-algebraic equations in mechanics.