Linearized methods for ordinary differential equations
type: Item
instance of: scholarly article
title: Linearized methods for ordinary differential equations
zbMATH Open document ID: 0935.65071
DOI: 10.1016/S0096-3003(98)10056-5
published in: Applied Mathematics and Computation
publication date: 1999-12-02T00:00:00Z
review text: The linearized \(\Theta\)-techniques and time-linearized methods for the solution of ordinary differential equations are considered. It is shown that both methods are implicit and provide explicit maps, but they do not preserve the energy in conservative systems. It is also shown that time-linearized methods preserve both fixed points and the linear stability of the original ordinary differential equation, whereas linearized \(\Theta\)-techniques do preserve the fixed points and the linear stability of attractors, but the stability of the repellers depends on the time step and the implicitness parameter. The results indicate that the linearized \(\Theta\)-techniques which more faithfully reproduce the nonlinear dynamics of the original ordinary differential equation are second-order accurate in time.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L07
zbMATH DE Number: 1355409
zbMATH Keywords: time-linearized methods
zbMATH Keywords: linearized \(\varTheta\)-techniques
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: Padé approximants
zbMATH Keywords: time-reversed logistic equation
zbMATH Keywords: fixed points
zbMATH Keywords: stability
zbMATH Keywords: attractors
zbMATH Keywords: repellers
author: Juan I. Ramos
reviewed by: Karel Najzar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1355409