On substantiation of a numerical method to solve nonlinear eigenvalue problems arising in electromagnetics

Background. The paper is devoted to nonlinear Sturm-Liouville problems. These problems arise in the theory of waveguides. The main goal is to justify a numerical method to calculate approximated eigenvalues. Materials and methods. The classical and modern methods of ordinary differential equations are applied. Results. The global unique solvability of Cauchy problems corresponding to the studied problems is proved. This result allows one to justify a numerical method based on shooting by the spectral parameter. Conclusions. This numerical method is an effective tool for computation approximated eigenvalues .