Steep gravity waves: Havelock’s method revisited

Gravity waves propagating at the surface of a fluid of infinite depth are considered. The problem is formulated in terms of a series expansion attributable to Havelock [Proc. R. Soc. London Ser. A 95, 38 (1919)]. The series is truncated after a finite number of terms and the unknown coefficients are found by collocation. It is shown that this simple numerical procedure yields accurate results for waves of arbitrary steepness.