Vladislav V. Kravchenko, Sergii M. Torba
Published 2013-06-12, updated 2014-04-29Version 3
A method for approximate solution of spectral problems for Sturm-Liouville equations based on the construction of the Delsarte transmutation operators is presented. In fact the problem of numerical approximation of solutions and eigenvalues is reduced to approximation of a primitive of the potential by a finite linear combination of generalized wave polynomials introduced in arXiv:1208.5984, arXiv:1208.6166. The method allows one to compute both lower and higher eigendata with an extreme accuracy.
Comments: 32 pages, 9 figures, 4 tables; Sections 6 and 7 extended, runtimes added
Subjects: 34A45,
34B09,
34B24,
34E05,
34L16,
34L40,
41A30,
41A50,
41A55,
65D30,
65L05,
65L15,
65L99,
81Q05
Analytic approximation of transmutation operators and related systems of functions
Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems
Analytic approximation of transmutation operators for one-dimensional stationary Dirac operators and applications to solution of initial value and spectral problems
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