Prikazchikov, V. G.; Allanazarov, Zh. P. Precising the solutions in a discrete spectral problem. (Russian) Zbl 0716.65076 Vychisl. Prikl. Mat., Kiev 69, 56-63 (1989). A method of rising the accuracy is considered for an one-dimensional spectral problem with variable coefficient. The precision formula is established by considering the leading term of the expansion of the eigenvalue error. A scheme of fourth order of accuracy is constructed which distinguishes from the scheme of second order of accuracy only by perturbation in the diagonal elements. The scheme is simple in realization. Cited in 1 Review MSC: 65L15 Numerical solution of eigenvalue problems involving ordinary differential equations 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators Keywords:one-dimensional spectral problem; variable coefficient; fourth order of accuracy PDFBibTeX XMLCite \textit{V. G. Prikazchikov} and \textit{Zh. P. Allanazarov}, Vychisl. Prikl. Mat. 69, 56--63 (1989; Zbl 0716.65076)