Explicit Numerial Iterative Methods Applied to the Three-Parameter Infiltration Equation

Finding explicit solutions to the partial differential equations governing the infiltration phenomenon tend to be a challenging issue. On account of such complexity, researchers have proposed algebraic equations to model this phenomenon. This paper deals with the solution of the general three-parameter infiltration equation, which is an implicit equation corresponding to the interpolation between the Green-Ampt and Talsma-Parlange infiltration models. By means of the Householders method, the cumulative infiltration is obtained by a rapidly converging iterative procedure. The results are further manipulated in order to obtain the infiltration rate explicitly. The effect of variables involved on the solution is also discussed. A case study is included to demonstrate the use of the proposed algorithm. The formulas proposed provide easy-to-use equations which enable calculations on the fly while considering practical applications.