An explicit energy-conserving numerical method for equations of the form \(d^ 2x/dt^ 2=f(x)\)
type: Item
instance of: scholarly article
title: An explicit energy-conserving numerical method for equations of the form \(d^ 2x/dt^ 2=f(x)\)
zbMATH Open document ID: 0667.65063
DOI: 10.1016/0021-9991(88)90027-7
author: Chaoyu Qin
published in: Journal of Computational Physics
publication date: 1988-01-01T00:00:00Z
review text: For the numerical integration of initial-value problems modelling physical problems one may look for methods that are energy conserving because conservation laws are fundamental in physics. For the simple initial value problem \((1)\quad d^ 2x/dt^ 2=f(x);\quad x(0)=\alpha,\quad dx/dt|_{t=0}=\beta\) the energy conservation equation is obviously expressed as (2) \(1/2(dx/dt)^ 2+\phi (x)=1/2\beta^ 2+\phi (\alpha)\) where \(\phi\) is defined by \(-(d\phi /dx)=f(x)\). \textit{D. Greenspan} [J. Comput. Phys. 56, 28-41 (1984; Zbl 0561.65056)] developed two methods for the problem (1) with the conservation relation (2), but this methods are implicit forms and require iterative calculations. The present author suggests an explicit numerical method of energy conserving type and gives some numerical examples.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4092687
zbMATH Keywords: explicit energy-conserving numerical method
zbMATH Keywords: numerical examples
reviewed by: Hans Ade
MaRDI profile type: Publication
full work available at URL: 0021-9991(88)90027-7
OpenAlex ID: W2043283724
cites work: Conservative numerical methods for \(\ddot x=f(x)\)
description: scientific article; zbMATH DE number 4092687