A Simple Analytical Solution for the Boussinesq One‐Dimensional Groundwater Flow Equation

An approximate analytical solution to the Boussinesq equation is presented here. Uniform initial conditions and a step function increase of piezometric head on the boundary are assumed. The one‐dimensional problem is reduced to an ordinary differential equation through Boltzmann's transformation, and a technique exploiting some basic characteristics of the exact solution leads to an approximate polynomial solution of the problem. The technique presented here can also be applied to one‐dimensional nonlinear diffusion problems. A numerical procedure incorporating some of the analytical characteristics of the exact solution is presented. A discussion concludes the paper.