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Numerical methods for higher order Sturm-Liouville problems. (English) Zbl 0970.65087

The authors review some efficient numerical methods for certain classes of linear selfadjoint and non-selfadjoint eigenvalue problems, respectively, where they concentrate on methods treated in their own work. For a class of \(2m\)th-order selfadjoint problems, the numerical schemes yield approximations to eigensolutions and to the counting function \(N(\lambda)\) as well. For a class of non-selfadjoint problems exhibiting the so-called Birkhoff regularity, the numerical code can find eigenvalues \(\lambda\) in a rectangular, left half plane, or vertical strip. Numerical results are presented.

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
34B24 Sturm-Liouville theory

Software:

SLEUTH; aicm
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References:

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