Twenty years of asymptotic correction for eigenvalue computation
Alan L. Andrew
(Received 7 August 2000)
Abstract
Asymptotic correction, first studied systematically in the 1979 ANU
thesis of John Paine, can significantly increase the accuracy and
efficiency of finite difference and finite element methods for
computing eigenvalues, especially higher eigenvalues, of differential
operators. It has proved especially useful for the solution of
inverse eigenvalue problems. This paper reviews the impact of this
method, and also presents some new numerical results which support a
recent conjecture of the author concerning the use of asymptotic
correction with Numerov's method for problems with natural boundary
conditions.