Computer-Algebraic Study of the Asymptotic Method for Modeling Waveguide Propagation of Electromagnetic Radiation

This paper formulates an asymptotic method for investigating vector electromagnetic fields of waveguide modes in the adiabatic approximation. The asymptotic method in the zero approximation is reduced to the symbolic investigation of a homogeneous system of ordinary differential equations; higher approximations correspond to inhomogeneous systems of ordinary differential equations with a similar matrix of coefficients. Using the asymptotic method, symbolic solutions in the zero and first approximations are obtained.