On a numerical method for solving nonlinear eigenvalue problems in the theory of TM-waves propagation in plane waveguides filled with a nonlinear medium

Background. The paper is devoted to nonlinear eigenvalue problems for nonlinear ordinary differential equations. These problems arise in the theory of propagation of TM waves in plane waveguides. The main goal is to justify a numerical method to calculate approximated eigenvalues and eigenfunctions. Materials and methods. Classical and modern methods of ordinary differential equations are used. 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 .