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Uniform estimation of the eigenvalues of Sturm–Liouville problems

Published online by Cambridge University Press:  17 February 2009

John Paine  and
Frank de Hoog
John Paine
Affiliation:
Computing Research Group, Australian National University, P.O. Box 4, Canberra, A.C.T. 2600, Australia
Frank de Hoog
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Yarralumla, A.C.T. 2600, Australia
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Abstract

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The perturbation of the eigenvalues of a regular Sturm–Liouville problem in normal form which results from a small perturbation of the coefficient function is known to be uniformly bounded. For numerical methods based on approximating the coefficients of the differential equation, this result is used to show that a better bound on the error is obtained when the problem is in normal form. A method having a uniform error bound is presented, and an extension of this method for general Sturm–Liouville problems is proposed and examined.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 3 , January 1980 , pp. 365 - 383
Copyright
Copyright © Australian Mathematical Society 1980

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