Collocation approximation to eigenvalues of an ordinary differential equation: numerical illustrations

We display the numerical results associated with the collocation of three eigenvalue problems using from one to four Gauss points per partition interval in order to document the sharpness of the error bounds we have previously obtained. The ordinary differential operators involved are real with cons...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics of computation 1981-01, Vol.36 (153), p.1-19
Main Authors: de Boor, Carl, Swartz, Blair
Format: Article
Language:English
Subjects:
Algebra
Approximation
Boundary conditions
Coefficients
Eigenfunctions
Eigenvalues
Ordinary differential equations
Polynomials
Textual collocation
Zero
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We display the numerical results associated with the collocation of three eigenvalue problems using from one to four Gauss points per partition interval in order to document the sharpness of the error bounds we have previously obtained. The ordinary differential operators involved are real with constant coefficients; two of the problems have an eigenvalue whose ascent exceeds one. We propose an explanation for the observed manner in which a set of simple approximate eigenvalues can approach a single multiple eigenvalue.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1981-0595038-4