Collocation approximation to eigenvalues of an ordinary differential equation: the principle of the thing
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- by Carl de Boor and Blair Swartz PDF
- Math. Comp. 35 (1980), 679-694 Request permission
Abstract:
It is shown that simple eigenvalues of an mth order ordinary differential equation are approximated within $\mathcal {O}(|\Delta {|^{2k}})$ by collocation at Gauss points with piecewise polynomial functions of degree $< m + k$ on a mesh $\Delta$. 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.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp. 35 (1980), 679-694
- MSC: Primary 65L15
- DOI: https://doi.org/10.1090/S0025-5718-1980-0572849-1
- MathSciNet review: 572849