Twenty years of asymptotic correction for eigenvalue computation

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.