Abstract
This study uses the combined Laplace transform and variational iteration method to analytically solve initial value problems (IVPs) and boundary value problems (BVPs) of Lane- Emden- equation with singular behaviour at . Initially, this method requires calculating the lagrange multiplayer, and after its value was calculated, it was found to be equal , this method is applying on several problems and the results were improved using Padé approximations, the results were compared with the exact solution by calculating the absolute error value between them.
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