Algorithms for evaluating basic components of spectral functions of interference wave fields

Simple algorithms for finding a numerical solution on a complex plane of dispersion equations dependent on a real parameter are described. Algorithms for numerical integration along stationary contours on a complex plane in the case where the integrand possesses singularities of the pole and branch-point type are also presented. These algorithms are applied to compute the spectral functions of wave fields propagating in layered media. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 214, 1994, pp. 187–199. Translated by N. S. Zabavnikova.