Volume 11, Issue 3, August 2004, Pages 276 - 288
A Family of Linearizations of Autonomous Ordinary Differential Equations with Scalar Nonlinearity
Received 21 November 2003, Accepted 8 April 2004, Available Online 1 August 2004.
- https://doi.org/10.2991/jnmp.2004.11.3.1How to use a DOI?
- 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.
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Cite this article
TY - JOUR AU - Fethi BELKHOUCHE PY - 2004 DA - 2004/08 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 - BELKHOUCHE2004 ER -