Open AccessA fast, new computational algorithm for free oscillations and surface waves
Author(s) -
Wiggins Ralph A.
Publication year - 1976
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1976.tb01266.x
Subject(s) - hermite polynomials , mathematics , mathematical analysis , eigenvalues and eigenvectors , basis (linear algebra) , basis function , surface (topology) , boundary value problem , polynomial , boundary (topology) , free surface , geometry , physics , quantum mechanics
Summary 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 –s̀ 2 B) c = 0 that can be solved by a variety of standard techniques.