Collocation Approximation to Eigenvalues of an Ordinary Differential Equation: The Principle of the Thing.
Abstract
It is shown that simple eigenvalues of an m-th order ordinary differential equation are approximated within 0(absolute value of delta to the 2k power) by collocation at Gauss points with piecewise polynomial functions of degree is less than m plus 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1979
- Accession Number
- ADA070197
Entities
People
- Blair Swartz
- Carl R. de Boor
Organizations
- University of Wisconsin–Madison