Numerical solutions of underwater acoustic wave propagation problems

Two accurate and general purpose numerical approaches are presented for the solution of variable‐coefficient parabolic wave equations. (1) An Ordinary Differential Equation Approach: The parabolic equation is treated as a system of ordinary differential equations where the second partial derivative with respect to the space variable is discretized by means of a second‐order central difference. Nonlinear Multistep (NLMS) methods are used as predictor and corrector for solving this system. A variable‐step‐size technique is built in to give the desired accuracy. The theory with regard to consistency, stability, and convergence has been very well developed for NLMS methods thus ensuring the convergence of this procedure. (2) A Finite‐Difference Approach: A finite‐difference technique is derived from the conventional implicit schemes. This technique is proved to be convergent in theory and is found to be general purpose and provides reasonable accuracy. The solution of a range‐dependent problem with nonflat bo...