The work discussed in the present paper was undertaken in response to difficulties experienced with numerical integration approaches. The technique involves the modeling of the medium as a set of horizontal strata in which the ambient gas parameters are ‘nearly’ constant, i.e., slowly varying. A perturbation theory allows us to take into account the slow vertical variation in a purely analytical way that is based on a knowledge of the system-equation solutions for a homogeneous medium. The computer is used to find eigenvalues of the system matrix and to provide the numerical coefficients for the solution matrix, which is expressed analytically as a function of z, the vertical distance coordinate. Illustrative numerical results are presented that show eigenvalues (corresponding to modes of propagation) and certain elements of the solution matrix for a typical ionospheric parameter regime.