ANZIAM J. 44(E) ppC1--C19, 2003.

Asymptotic correction of Numerov's eigenvalue estimates with general boundary conditions

Abstract

The error in the estimate of the kth eigenvalue of -y¢¢+qy=ly, y(0)=y(p)=0, obtained by Numerov's method with uniform step length h, is O(k⁶ h⁴ ). The author and J. Paine showed that a correction technique of Paine, de Hoog and Anderssen reduced this to O(k⁴ h⁵ /sin(kh)), with negligible extra effort. Later the author extended the method to deal with boundary conditions of the form y¢(a)=0. This paper shows how a similar increase in accuracy can be obtained, with a little more effort, for problems with one or more boundary conditions of the form y¢(a)=ay(a) where a ¹ 0 .

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Authors

Alan L. Andrew

Mathematics Department, La Trobe University, Victoria 3086, Australia. mailto:a.andrew@latrobe.edu.au

Published 1 April 2003, amended April 11, 2003. ISSN 1446-8735