A fast, new computational algorithm for free oscillations and surface waves

Abstract

The solution for the periods of the free oscillations of a sphere or for the phase velocity of surface waves on a half‐space is an example of a two‐point boundary value problem. A stable and efficient method for solving such problems is a Rayleigh–Ritz variational procedure. The solution functions are approximated by a sum of a finite number of Hermite polynomial basis functions. The coefficients of the basis functions are determined by minimizing the Lagrangian. This process leads to an eigenvalue problem of the form (A –s̀2 B) c = 0 that can be solved by a variety of standard techniques. Copyright © 1976, Wiley Blackwell. All rights reserved