Finite Element Method (FEM), based on p and h versions approach, and the Adomians decomposition algorithm (ADM) are introduced for solving the Emden-Fowler Equation. A number of special cases of p and h versions of FEM are introduced. Several iterated forms of the ADM are considered also. To demonstrate the efficiency of both methods, the numerical solutions of different examples are compared for both methods with the analytical solutions. It is observed that the results obtained by FEM are quite satisfactory and more accurate than ADM. Moreover, the FEM method is applicable for a wide range of classes including the singularity cases with the given special treatments by the FEM. Comparing the results with the existing true solutions shows that the FEM approach is highly accurate and converges rapidly.
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