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

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 Khmelnytskaya et al. (2013), and Kravchenko and Torba (2014). The method allows one to compute both lower and higher eigendata with an extreme accuracy.