Green and Ampt infiltration equation: comparison of two analytic direct methods

The explicit solutions of the Green and Ampt infiltration equation, by developing a modified Adomian Decomposition Method (MADM) and Variational Iteration Method (VIM) solution with an exact solution, are compared. These solutions were compared with the exact implicit solution and a good trend between our approaches and the exact solution was found.  The best result is gained by only the first three terms in the series solutions of MADM. As the number of terms increases, the error in the lower bound of the computational domain grows and the upper bound converges after the first three terms of MADM. On the other hand, variational iteration converges after the first two terms. Both methods addressing this phenomenon seem quite promising, and by considering only a few terms the results are accurate, making both methods fast and efficient.