A Representation for Solutions of Sturm-Liouville Equations and its Application for Solving Boundary Value and Spectral Problems

Journal Article · Mon Sep 01 04:00:00 EDT 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2991015· OSTI ID:21251348

Kravchenko, Vladislav V ^[1]

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1. 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, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1048; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTIC FUNCTIONS
APPROXIMATIONS
BOUNDARY-VALUE PROBLEMS
FUNCTIONAL ANALYSIS
MATHEMATICAL OPERATORS
NUMERICAL SOLUTION
POLYNOMIALS
SCHROEDINGER EQUATION
STURM-LIOUVILLE EQUATION
TWO-DIMENSIONAL CALCULATIONS