Finite-difference solution to the parabolic wave equation

In this article an implicit finite-difference (IFD) scheme is introduced for solving underwater acoustic wave propagation problems. This scheme is applied to the parabolic wave equation model for the acoustic problem with a free surface and arbitrary bottom and bottom boundary conditions. The mathematical theory of the implicit finite-difference method as applied to the parabolic equation is developed, and a computer model to implement the IFD is introduced. Representative problems are presented to demonstrate the capability of the IFD model. Advantages and limitations of the IFD are discussed.