On the use of rootfinding ODE software for the solution of a common problem in nonlinear dynamical systems
type: Item
instance of: scholarly article
title: On the use of rootfinding ODE software for the solution of a common problem in nonlinear dynamical systems
zbMATH Open document ID: 0685.65060
DOI: 10.1016/0377-0427(89)90334-8
author: K. Appert
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: This paper describes a FORTRAN code PLOD by \textit{E. Agron}, \textit{G. Gunaranta}, the first author and \textit{M. A. Reed} [Mathematical software: PLOD, plotted solutions of differential equations, IEEE Micro 8(4) (1988)] for the numerical solution of ordinary differential equations (ODEs), which is particularly suited to calculate Poincaré sections for nonlinear models of dynamics and includes graphics capabilities. The code PLOD is based on Adams and Gear formulas with variable step and variable order, and it has also the so called g-stop facility which allows to stop the integration when some prescribed auxiliary conditions of interest are satisfied. In the paper, the authors briefly outline the possibilities of PLOD in studying numerically some dynamical systems which arise in several problems of real life. In particular, the bifurcations in the model of \textit{V. Franceschini} [Physica D 6, 285--304 (1983; Zbl 1194.34075)] are computed.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34-04
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 4123190
zbMATH Keywords: FORTRAN code PLOD
zbMATH Keywords: Poincaré sections
zbMATH Keywords: Adams and Gear formulas
zbMATH Keywords: variable step
zbMATH Keywords: variable order
zbMATH Keywords: dynamical systems
zbMATH Keywords: bifurcations
Wikidata QID: Q111897669
describes a project that uses: pchip
describes a project that uses: UNCMND
describes a project that uses: FORSIM VI
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90334-8
OpenAlex ID: W2052702735
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description: scientific article; zbMATH DE number 4123190