Numerical Study of One - Dimensional Ground Water Recharge through Porous Media with Linear Permeability

The present paper deals with the approximate solution of one dimensional ground water recharge problem through porous media with linear permeability. The phenomenon is formulated using Gauss Elimination Method. . This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem. The Gauss Elimination Method (GEM) has been shown to solve effectively, easily and accurately a large class of linear problem with approximations converging rapidly to exact solutions. The solution of nonlinear partial differential equation by using finite element method, is in the term of ascending series and it is obtained by using Matlab and Mathematica.