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For contractive interval functions $[g]$ we show that $[g] ({[x]}_{ϵ}^{k_{0}}) \subseteq \int ({[x]}_{ϵ}^{k_{0}})$ results from the iterative process ${[x]}^{k + 1} : = [g] ({[x]}_{ϵ}^{k})$ after finitely many iterations if one uses the epsilon-inflated vector ${[x]}_{ϵ}^{k}$ as input for $[g]$ instead of the original output vector ${[x]}^{k}$ . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

Equilibria of Runge-Kutta methods.

E. Hairer, J.M. Sanz-Serna, A. Iserles (1990/1991)

Numerische Mathematik

Erratum: On the convergence of multistep methods for nonlinear stiff differential equations.

Lubich. C. (1992)

Numerische Mathematik

Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics

Othmar Koch, Christof Neuhauser, Mechthild Thalhammer (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

McDonald, Edward J., Higham, Desmond J. (2001)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Error Bounds for Numerical Solutions of Ordinary Differential Equations.

G.J. Cooper (1971/1972)

Numerische Mathematik

Error estimates and step-size control for the approximate solution of a first order evolution equation

Günter Lippold (1991)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Error estimates of a numerical method for a class of nonlinear evolution equations

Mircea Sofonea (1993)

Revista colombiana de matematicas

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.

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Efficient Runge-Kutta methods for Hamiltonian equations

Eine Aussage über Alternanten.

Einschließungsaussagen für gewöhnliche Differentialoperatoren. -Range-Domain Implications for Ordinary Differential Operators.

Energy and Momentum Conserving Methods of Arbitrary Order for the Numerical Integration of Equations of Motion. II. Motion of a System of Particles.

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

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

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 $G$ -Stabilitätsbegriffes auf die Klasse der linearen Mehrschrittblockverfahren.

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.

Currently displaying 1 – 20 of 25