Abstract
Water waves in water of arbitrary depth and solitary waves are calculated numerically using new series truncation methods. The techniques use a refinement of Davies’ approximation first proposed by Tulip. Accurate numerical solutions are obtained for all values of the steepness up to the limiting configuration with a $120^ \circ $ angle at the wave crest. It is shown that the proposed numerical procedure is equivalent to the method of Havelock. The method of Michell is included as a particular case. A comparison with previous numerical methods, such as boundary integral equation techniques, is given.
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