Extrapolation of symplectic methods for Hamiltonian problems
type: Item
instance of: scholarly article
title: Extrapolation of symplectic methods for Hamiltonian problems
zbMATH Open document ID: 0951.65138
DOI: 10.1016/S0168-9274(99)00127-0
published in: Applied Numerical Mathematics
publication date: 2000-12-06T00:00:00Z
review text: Recently, symplectic Runge-Kutta methods used with constant stepsize have been shown to exhibit linear error growth when applied to certain classes of Hamiltonian systems over long time intervals. This paper addresses the problem of the length of the integration interval over which extrapolation will improve the numerical solution. The authors consider two models of the extrapolation of symplectic and symmetric numerical integrators. In the passive mode, two solution sequences are computed with different stepsizes independently and extrapolation is performed whenever output is required. In the active mode, the extrapolation is carried out at each step and the extrapolated solution is then propagated. Both modes of extrapolation are studied in detail and compared for the simple harmonic oscillator.
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 37J35
zbMATH DE Number: 1462298
zbMATH Keywords: symplectic methods
zbMATH Keywords: integrable Hamiltonian system
zbMATH Keywords: active extrapolation
zbMATH Keywords: passive extrapolation
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: harmonic oscillator
author: R. P. K. Chan
author: Ander Murua
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: s0168-9274(99)00127-0
OpenAlex ID: W2079763265
description: scientific article; zbMATH DE number 1462298