A Representation for Solutions of Sturm-Liouville Equations and its Application for Solving Boundary Value and Spectral Problems
- Departamento de Matematicas, CINVESTAV del IPN, Unidad Queretaro, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, Queretaro, Qro. C.P. 76230 (Mexico)
In [4] a new representation for solutions of the Sturm-Liouville equation (pu')'+qu = {omega}{sup 2}u in terms of a nontrivial solution of (pu{sub 0}{sup '})'+qu{sub 0} 0 was obtained with the aid of the theory of pseudoanalytic functions and their relationship to solutions of the stationary two-dimensional Schroedinger equation. The representation has a simple and easily verifiable form and lends itself to numerical computation. We discuss its applications to numerical solution of corresponding boundary value and spectral problems. For example, using this representation a spectral Sturm-Liouville problem reduces to finding zeros of an analytic function whose Taylor coefficients are constructed explicitly.
- OSTI ID:
- 21251348
- Journal Information:
- AIP Conference Proceedings, Vol. 1048, Issue 1; Conference: International conference on numerical analysis and applied mathematics 2008, Psalidi, Kos (Greece), 16-20 Sep 2008; Other Information: DOI: 10.1063/1.2991015; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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