A Gautschi-type method for oscillatory second-order differential equations
type: Item
instance of: scholarly article
title: A Gautschi-type method for oscillatory second-order differential equations
zbMATH Open document ID: 0937.65077
author: Marlis Hochbruck
author: Christian Lubich
published in: Numerische Mathematik
publication date: 2000-06-07T00:00:00Z
full work available at URL: https://publikationen.bibliothek.kit.edu/1000042296
review text: The authors study a numerical method for second-order differential equations in which high-frequency oscillations are generated by a linear part. The scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly (Gautschi-type method). It is proved that the method admits second-order error bounds which are independent of the product of the stepsize with the frequencies. Results of numerical experiments with the sine-Gordon equation are included.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1355440
zbMATH Keywords: Gautschi-type method
zbMATH Keywords: oscillatory second-order differential equations
zbMATH Keywords: high-frequency oscillations
zbMATH Keywords: error bounds
zbMATH Keywords: numerical experiments
zbMATH Keywords: sine-Gordon equation
reviewed by: K. T. S. Iyengar
MaRDI profile type: Publication
OpenAlex ID: W1989947528
DOI: 10.1007/S002110050456
description: scientific article; zbMATH DE number 1355440