Asymptotic Methods in Non Linear Dynamics

Abstract

This paper features and elaborates recent developments and modifications in asymptotic techniques in solving differential equation in non linear dynamics. These methods are proved to be powerful to solve weakly as well as strongly non linear cases. Obtained approximate analytical solutions are valid for the whole solution domain. In this paper, limitations of traditional perturbation methods are illustrated with various modified techniques. Mathematical tools such as variational approach, homotopy and iteration technique are discussed to solve various problems efficiently. Asymptotic methods such as Variational Method, modified Lindstedt-Poincare method, Linearized perturbation method, Parameter Expansion method, Homotopy Perturbation method and Perturbation-Iteration methods(singular and non singular cases) have been discussed in various situations. Main emphasis is given on Singular perturbation method and WKB method in various numerical problems.