Latest Developments in Nonlinear Sciences

This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method