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Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems | Vladislav V. Kravchenko
; Samy Morelos
; Sergii M. Torba
; | Date: |
17 Dec 2014 | Abstract: | A method for solving spectral problems for the Sturm-Liouville equation
$(pv^{prime})^{prime}-qv+lambda rv=0$ based on the approximation of the
Delsarte transmutation operators combined with the Liouville transformation is
presented. The problem of numerical approximation of solutions and of eigendata
is reduced to approximation of a pair of functions depending on the
coefficients $p$, $q$ and $r$ by a finite linear combination of certain
specially constructed functions related to 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. Several
necessary results concerning the action of the Liouville transformation on
formal powers arising in the method of spectral parameter power series are
obtained as well as the transmutation operator for the Sturm-Liouville operator
$frac{1}{r}left(frac{d}{dx}pfrac{d}{dx}-q
ight)$. | Source: | arXiv, 1412.5237 | Services: | Forum | Review | PDF | Favorites |
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