Journal of Nonlinear Mathematical Physics

Volume 11, Issue 3, August 2004, Pages 276 - 288

A Family of Linearizations of Autonomous Ordinary Differential Equations with Scalar Nonlinearity

Authors
Fethi BELKHOUCHE
Corresponding Author
Fethi BELKHOUCHE
Available Online 9 December 2006.
DOI
https://doi.org/10.2991/jnmp.2004.11.3.1How to use a DOI?
Abstract
This paper deals with a method for the linearization of nonlinear autonomous diferential equations with a scalar nonlinearity. The method consists of a family of approximations which are time independent, but depend on the initial state. The family of linearizations can be used to approximate the derivative of the nonlinear vector field, especially at equilibrium points, which are of particular interest, it can be used also to determine the asymptotic stability of equilibrium point, especially in the non-hyperbolic case. Using numerical experiments, we show that the method presents good agreement with the nonlinear system even in the case of highly nonlinear systems.
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
11 - 3
Pages
276 - 288
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2004.11.3.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Fethi BELKHOUCHE
PY  - 2006
DA  - 2006/12
TI  - A Family of Linearizations of Autonomous Ordinary Differential Equations with Scalar Nonlinearity
JO  - Journal of Nonlinear Mathematical Physics
SP  - 276
EP  - 288
VL  - 11
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.3.1
DO  - https://doi.org/10.2991/jnmp.2004.11.3.1
ID  - BELKHOUCHE2006
ER  -