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.


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


SLEUTH; aicm
Full Text: DOI


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