A Review Article On Mathematical Aspects Of Nonlinear Models

Abstract

The main objective of this review article is to propose some mathematical aspects of nonlinear models. In mathematics, nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account. Nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects. Contrary to traditional modelling methods, such as linear regression and basic statistical methods, nonlinear modelling can be utilized efficiently in a vast number of situations where traditional modelling is impractical or impossible. This review article mainly explores on mathematical preliminaries of nonlinear models, solution of algebraic and transcendental equations and solution of system of nonlinear equations. In addition to these Taylor polynomial and finite difference operators, least - squares polynomial approximation and the roots of the equations are also discussed here.