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Eigenvalue Enclosures for Ordinary Differential Equations

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Inclusion Method
Numerical Example
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Keywords Upper and lower bounds to eigenvalues - Rayleigh-Ritz method - Lehmann-Maehly method

Selfadjoint eigenvalue problems for ordinary differential equations are very important in the sciences and in engineering. The characterization of eigenvalues by a minimum-maximum principle for the Rayleigh quotient forms the basis for the famous Rayleigh-Ritz method . This method allows for an efficient computation of nonincreasing upper eigenvalue bounds. N.J. Lehmann and H.J. Maehly [6,7,8] independently developed complementary characterizations that can be used to compute lower bounds. These methods are based on extremal principles for the Temple quotient . In general, however, an application of the Lehmann-Maehly method requires that certain quantities can be determined explicitly. This may be difficult or even impossible when dealing with