Abstract—The aim of this paper is to present a generalization of the optimal linearization. This method enables us to associate a linear map to a nonlinear ordinary differential equation. Our results show clearly the existence and the unicity of the best optimal linearization in the sense of the least square. We use an approach to associate a linear optimal equation to a nonlinear equation in the neighbourhood of zero, even though the equation cannot be linearized around the origin using the Frechet derivative. An application is done to analyze the behaviour of an electronic circuit.

Index Terms—Electronic circuit, Least square approximation, Nonlinear ODE, Optimal linearization.

A. Chikhaoui is with the Modeling laboratory, Department of physics, University of Tlemcen, B.p. 119, Tlemcen R.p 13000, Algeria.
T. BENOUAZ, was with the Modeling laboratory, Department of physics, University of Tlemcen, B.p. 119, Tlemcen R.p 13000, Algeria.
A. CHEKNANE is with Laboratoire de Valorisation des Energies Renouvelables et Environnements Agressifs, Electrical Engineering Department, University Amar Telidji Laghouat R.P 03000, Algérie(Mobile:+213 (+213) 7 78 35 02 82, Fax:(+213) 29 93 26 98

Cite: A. Chikhaoui, T. Benouaz, and A. Cheknane, "Computational Approach of the Optimal Linearization of the Nonlinear O.D.E: Application to Nonlinear Electronic Circuit," International Journal of Computer and Electrical
Engineering vol. 1, no. 2, pp. 136-141, 2009.