In this paper we present several set of solutions static and spherically symmetric solitonic boson stars. Each is characterized by the value {\sigma} that defines potential in complex scalar field theory. The main features peculiar to occur for small values {\sigma}, but which equations become so stiff as pose numerical challenges. Without making approximations build sets decreasing show how th...

The Carathéodory approximation scheme was introduced by the Greek mathematician named Constantine Carathéodory in the early part of 20th century for ordinary differential equations (Chapter 2 of [1]). Later this was extended by Bell and Mohammad to stochastic differential equations [2] and then by Mao [3, 4]. Generally, the solutions of stochastic differential equations (SDEs) do not have expli...

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...