Approximate analytical solution of the Boussinesq equation with numerical validation

A new approximate solution of the one-dimensional Boussinesq equation is pr esented for a semi-infinite aquifer when the hydraulic head at the source i s an arbitrary function of time. Estimates for recharge, discharge, and ele vation of the water table are given. The simplicity and accuracy of the app roximation are compared with "exact" numerical and analytical solutions. Th e method of solution is illustrated with several examples including the com monly treated case of a constant boundary head and a nonmonotonically varyi ng boundary head.