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Automatic Solution of the Sturm-Liouville Problem

Automatic Solution of the Sturm-Liouville Problem Automatic Solution of the Sturm-Liouville Problem P B. BAILEY, M. K. GORDON, and L. F SHAMPINE Sand)a Laborator)es A general purpose algorithm is described for the automatic computation of eigenvalues and eigenfunctions of Sturm-Llouvllle problems, both singular and nonsmgular The method is based on the solution of initial value problems, using an integrator with a built-in global error estimating capabihty Problems arising in the construction of a satisfactory algorithm for this task are described, as are some of the software engineering aspects The resulting algorithm has performed satisfactorily on a sizable list of test problems Key Words and Phrases" elgenvalues, eigenfunctions, Sturm-Liouville problem, singular boundary value problem, mathematical software CR Categories 3 1, 3 2, 5 16, 5 17 INTRODUCTION Although there have been many codes constructed for solving special types of Sturm-Liouville eigenvalue problems, both singular and nonsingular, there seem to be none which are widely applicable: singular problems seem to be treated on a case-by-case basis, as are the effects on the accuracy of the computed eigenvalue of such things as local integration tolerance or truncation of an infinite interval. No doubt any given scheme for computing eigenvalues of singular SturmLiouville problems can be made to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

Automatic Solution of the Sturm-Liouville Problem

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References (8)

Publisher
Association for Computing Machinery
Copyright
Copyright © 1978 by ACM Inc.
ISSN
0098-3500
DOI
10.1145/355791.355792
Publisher site
See Article on Publisher Site

Abstract

Automatic Solution of the Sturm-Liouville Problem P B. BAILEY, M. K. GORDON, and L. F SHAMPINE Sand)a Laborator)es A general purpose algorithm is described for the automatic computation of eigenvalues and eigenfunctions of Sturm-Llouvllle problems, both singular and nonsmgular The method is based on the solution of initial value problems, using an integrator with a built-in global error estimating capabihty Problems arising in the construction of a satisfactory algorithm for this task are described, as are some of the software engineering aspects The resulting algorithm has performed satisfactorily on a sizable list of test problems Key Words and Phrases" elgenvalues, eigenfunctions, Sturm-Liouville problem, singular boundary value problem, mathematical software CR Categories 3 1, 3 2, 5 16, 5 17 INTRODUCTION Although there have been many codes constructed for solving special types of Sturm-Liouville eigenvalue problems, both singular and nonsingular, there seem to be none which are widely applicable: singular problems seem to be treated on a case-by-case basis, as are the effects on the accuracy of the computed eigenvalue of such things as local integration tolerance or truncation of an infinite interval. No doubt any given scheme for computing eigenvalues of singular SturmLiouville problems can be made to

Journal

ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery

Published: Sep 1, 1978

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