Stationary phase and practical numerical evaluation of ship waves in shallow water

A simple and highly-efficient method for numerically evaluating the waves created by a ship that travels at a constant speed in calm water, of large depth or of uniform depth, is given. The method, inspired by Kelvin's classical stationary-phase analysis, is suited for evaluating far-field as well as near-field waves. More generally, the method can be applied to a broad class of integrals with integrands that contain a rapidly oscillatory trigonometric function with a phase function whose first derivative (and possibly also higher derivatives) vanishes at one or several points, commonly called points of stationary phase, with the range of integration.