  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.
