Inverse Sturm-Liouville Systems over the whole Real Line

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2010

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Altundağ, Hüseyin

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In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization techniques to overcome the ill-posedness difficulty. Moreover, since the problem is nonlinear the iterative solution procedures are needed. Direct computation of the eigenvalues in iterative solution is handled via psoudespectral methods. The numerical examples of the considered problem are given to illustrate the accuracy and convergence behaviour.

Subject Keywords

Numerical analysis.

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http://etd.lib.metu.edu.tr/upload/12612693/index.pdf
https://hdl.handle.net/11511/20031

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

H. Altundağ, “Inverse Sturm-Liouville Systems over the whole Real Line,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.