On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations
type: Item
instance of: scholarly article
title: On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations
zbMATH Open document ID: 1074.65097
author: Volker Grimm
published in: Numerische Mathematik
publication date: 2005-04-14T00:00:00Z
review text: The paper deals with the numerical analysis of highly oscillatory second-order differential equations with dominating linear term. Numerical standard schemes applied to such an equation are forced to use step sizes \(h\) smaller than the square root of the linear term. Using an appropriate formal representation of the exact solution the author derives a numerical scheme with exponential Gautschi-type integrators. For solutions satisfying a finite energy condition second-order convergence of the numerical scheme is shown. Here the constant is independent of the norm of the dominating linear term, that is, independent of the frequency of the exact solution. Integrators of that type are particularly well suited for the long-time integration of oscillatory second order differential equations. Finally, a numerical example from molecular dynamics is presented.
reviewed by: Johannes Schropp
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 2156012
zbMATH Keywords: oscillatory differential equations
zbMATH Keywords: exponential integrators
zbMATH Keywords: convergence
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: s00211-005-0583-8
OpenAlex ID: W1966068952
cites work: Q2712873
cites work: Modulated Fourier expansions of highly oscillatory differential equations
cites work: Long-Time-Step Methods for Oscillatory Differential Equations
cites work: Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
cites work: Q4531870
cites work: On Krylov Subspace Approximations to the Matrix Exponential Operator
cites work: A Gautschi-type method for oscillatory second-order differential equations
cites work: Exponential Integrators for Large Systems of Differential Equations
cites work: Think globally, act locally: Solving highly-oscillatory ordinary differential equations
cites work: Q4356577
DOI: 10.1007/S00211-005-0583-8
description: scientific article; zbMATH DE number 2156012