This survey is intended to give an overview of the existing numerical methods and techniques for solving a multi-parameter eigenvalue problem. It also collects some well-known examples of multi-parameter spectral problem and its practical applications in different scientific areas.
This paper is devoted to the solving an eigenvalue problem for opened layered cylindrical waveguide structure with arbitrary finite number coaxial magnetodielectric layers. Classical method of separation of variables for analitycal solution to a boundary value problem for second order non-self-adjoint differential operator is applied. A general solution for electromagnetic field components, its boundary and infinity conditions are applied to obtain the complex transcendental dispersion equation.