Abstract
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 Padé algorithm, which provides the capability of the finite-difference algorithm. For deep water problems, the split-step Padé algorithm provides efficiency comparable to the split-step Fourier algorithm. For the shallow water problems that are currently of interest, the split-step Padé algorithm can be more than an order of magnitude faster than the split-step Fourier algorithm.
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