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Numerical computation of eigenvalues of discontinuous Sturm-Liouville problems with parameter dependent boundary conditions using sinc method. (English) Zbl 1281.65105

The article is concerned with Sturm-Liouville eigenvalue problems with an additional interface condition at the midpoint of the underlying interval, and with the cigenvalue parameter occurring in the differential equation as well as in both boundary conditions. A transcendental equation for the eigenvalues, involving particular solutions, is put up. A numerical method based on sampling techniques is proposed for computing eigenvalue approximations, and error estimates are provided. Some numerical examples illustrate the results.

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

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