Collocation approximation to eigenvalues of an ordinary differential equation: the principle of the thing

Authors:
Carl de Boor and Blair Swartz

Journal:
Math. Comp. **35** (1980), 679-694

MSC:
Primary 65L15

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572849-1

MathSciNet review:
572849

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Abstract: It is shown that simple eigenvalues of an *m*th order ordinary differential equation are approximated within by collocation at Gauss points with piecewise polynomial functions of degree on a mesh . The same rate is achieved by certain averages in case the eigenvalue is not simple. The argument relies on an extension and simplification of Osborn's recent results concerning the approximation of eigenvalues of compact linear maps.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572849-1

Keywords:
Eigenvalues,
compact linear map,
ordinary differential equation,
collocation,
piecewise polynomial,
superconvergence

Article copyright:
© Copyright 1980
American Mathematical Society