Advances in Dynamical Systems and Applications
  • Year: 2007
  • Volume: 2
  • Issue: 1

On the Relationship between the Classical Linearization and Optimal Derivative*

  • Author:
  • Tayeb Benouaz1, Martin Bohner2
  • Total Page Count: 17
  • Page Number: 41 to 57

1Laboratoire de Modélisation, B.P. 119, Université Tlemcen, Tlemcen, 13000, Algérie. E-mail: t_benouaz@mail.univ-tlemcen.dz

2Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65409-0020, USA. E-mail: bohner@umr.edu

AMS subject classification: 34A30, 34A34.

Abstract

The aim of this paper is to present the relationship between the classical linearization and the optimal derivative of a nonlinear ordinary differential equation. An application is presented using the quadratic error.

Keywords

Classical linearization, Fréchet derivative, optimal derivative, quadratic error