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.