Iterative methods for the infiltration advance problem

We examine the in ltration advance problem in irrigation hydraulics modeled through the Lewis-Milne equation. We propose two iterative methods that give reasonable results compared with existing formulas for various well-known in ltration functions. The method of successive approximations seen as a xed-point method and the variational iteration method (based on Lagrange multipliers method) produce formulas after few iterations and simple calculations compared to existing methods where the Laplace transform of the in ltration function has to be known.