Ground-Water Flow Computations by Method of Lines

The Method of Lines has been applied successfully to the solution of the Boussinesq equation governing unconfined, saturated, transient ground-water flow. The time discrete-space continuous approach was chosen, and the PDE was converted to a set of ODE in space. The resulting set of two-point boundary value problems, one for each time level, was solved numerically by a shooting technique in connection with inverse interpolation. The method was found to be versatile, efficient, and easy to program. In two examples involving different boundary conditions, the numerical integration has been carried out utilizing a Runge-Kutta scheme on a computer and a simpler, second-order finite difference on a programmable hand-held calculator.