Thursday, June 13, 2013

1306.2914 (Vladislav V. Kravchenko et al.)

Analytic approximation of transmutation operators and applications to
highly accurate solution of spectral problems

Vladislav V. Kravchenko, Sergii M. Torba
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.
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