Comparison of algorithms for solving parabolic wave equations

The three types of algorithms that have been developed for solving parabolic wave equations are compared. Until recently, it was necessary to choose between the finite-difference and split-step Fourier algorithms and make a trade-off between efficiency and capability. Test problems are presented to illustrate the efficiency of the split-step Padi algorithm, which provides the capability of the finite-difference algorithm. For deep water problems, the split-step Pade algorithm provides efficiency comparable to the split-step Fourier algorithm. For the shallow water problems that are currently of interest, the split-step Pade algorithm can be more than an order of magnitude faster than the split-step Fourier algorithm.