Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method
type: Item
instance of: scholarly article
title: Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method
zbMATH Open document ID: 0707.65060
DOI: 10.1007/BF00945108
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1990-01-01T00:00:00Z
review text: An automated homotopy method, based on elementary estimates, is described for the computation of inclusion intervals for the first N eigenvalues of Sturm-Liouville problems with either separated or periodic boundary conditions. Interval arithmetic (with FORTRAN-SC subroutines) is used to deal with roundoff. The method requires the solution of a number of related eigenvalue problems using approximations to the coefficients. Unlike some methods which require solution of a single problem with approximations to the coefficients [the reviewer, Congr. Numerantium 34, 3-16 (1982; Zbl 0535.65060)], the method is stated to be readily generalized to partial differential equations, and a paper on this is foreshadowed.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 65H20
zbMATH DE Number: 4162184
zbMATH Keywords: second-order ordinary differential operators
zbMATH Keywords: automated homotopy method
zbMATH Keywords: inclusion intervals
zbMATH Keywords: Sturm-Liouville problems
zbMATH Keywords: Interval arithmetic
zbMATH Keywords: eigenvalue
author: Michael Plum
reviewed by: Alan L. Andrew
describes a project that uses: FORTRAN-SC
describes a project that uses: ACRITH-XSC
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4162184