On methods for the numerical solution of one spectral problem

In the paper a comparative analysis of some methods for numerical solution of spectral problems that can be used to solve optimization problems in nanoelectronics is used. One of the goals of the analysis is to study the possibility of using variational methods to solve spectral problems. This approach seems preferable when solving multidimensional problems. Comparison of methods is carried out on the example of solving a one-dimensional spectral problem. It is concluded that the numerical-analytical method is effective in the one-dimensional case, and the variational method is effective in the multidimensional case.