Invariant Imbedding and Unsteady Ground-Water Flow

The invariant imbedding technique is used to find the unknown slope of the water table near the surface reservoir in a problem of unsteady ground-water flow into a surface reservoir in a large unconfined aquifer. The original nonlinear two-point boundary-value problem is transformed into an initial-value problem and an exact solution is obtained by the technique of quasilinearization. The invariant imbedding method involves no trial-and-error procedure and is easily programmed. This technique provides a useful tool in solving field problems and it becomes extremely powerful in solving a family of problems in which a set of unknown initial conditions are required to be determined from the corresponding given set of boundary conditions.