Some Solution Methods for Lane-Emden Differential Equation when the Polytropic Index is Three

The Lane-Emden equation is one of the widely used and challenging equations in nonlinear dynamics. It is a central equation in the theory of steller structures. In this paper, Lane-Emden equation when has been solved using few different methods. Pade approximant has also been calculated of the obtained solution. The results obtained using semi-analytical methods are compared with the solutions obtained using well-known numerical methods namely Runge-Kutta’s fourth order method and ODE 45 graphically.