Double-Precision Evaluation of the Oscillatory Source Potential

Abstract

A table with double-precision accuracy is constructed for the three-dimensional source potential which occurs in the case of harmonic motion with zero forward-velocity beneath a linearized free surface. To facilitate the numerical integration, the source potential is expressed as the sum of a finite integral and of Bessel and Struve functions. Romberg quadrature is used to evaluate the finite integral, and the Bessel and Struve functions are evaluated by backward recursion.