Collocation Approximation to Eigenvalues of an Ordinary Differential Equation: The Principle of the Thing.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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It is shown that simple eigenvalues of an m-th order ordinary differential equation are approximated within 0absolute 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 Osborns recent results concerning the approximation of eigenvalues of compact linear maps.
- Numerical Mathematics