A general pseudospectral formulation of a class of Sturm-Liouville Systems

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2010
Alıcı, Haydar
In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schrödinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of square integrable functions. Pseudospectral methods based on this natural expansion basis are constructed to approximate the eigenvalues of WEHTP, and hence the energy eigenvalues of the Schrödinger equation. Exemplary computations are performed to support the convergence numerically.
Citation Formats
H. Alıcı, “A general pseudospectral formulation of a class of Sturm-Liouville Systems,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.