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

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Fethi Belkhouche
PY  - 2004
DA  - 2004/08/01
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  - 10.2991/jnmp.2004.11.3.1
ID  - Belkhouche2004
ER  -