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Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method. (English) Zbl 1080.34010
Here, the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter are computed. The purpose of this paper is twofold. First, a regularization avoiding any integration is considered. It is shown that one can get higher-order estimates on the eigenvalues at very low cost. The used method is called regularized sampling method and is an improvement of the method based on Shannon sampling theory. In the second place, the computation of the eigenvalues of Sturm-Liouville problems with quite general separated parameter dependent boundary conditions is tackled. A few examples are presented to illustrate the power of the method and a comparison is made with the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.

MSC:
34B24Sturm-Liouville theory
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
34B07Linear boundary value problems with nonlinear dependence