TY - JOUR
T1 - A family of linearizations of autonomous ordinary differential equations with scalar nonlinearity
AU - Belkhouche, Fethi
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2004
Y1 - 2004
N2 - This paper deals with a method for the linearization of nonlinear autonomous differential 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.
AB - This paper deals with a method for the linearization of nonlinear autonomous differential 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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U2 - 10.2991/jnmp.2004.11.3.1
DO - 10.2991/jnmp.2004.11.3.1
M3 - Article
AN - SCOPUS:6344262171
VL - 11
SP - 276
EP - 288
JO - Journal of Nonlinear Mathematical Physics
JF - Journal of Nonlinear Mathematical Physics
SN - 1402-9251
IS - 3
ER -