A new analytical technique for solving Lane - Emden type equations arising in astrophysics

Lane - Emden type equations are nonlinear differential equations which represent many scientific phenomena in astrophysics and mathematical physics. In this study, a new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary. Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for Lane Emden type equations.