  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.
