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A simulation algorithm is considered for the amplification of electromagnetic waves in a cylindrical waveguide with a plasma-dielectric filling. The field part of the problem is described by a Schrödinger-type equation for the polarization potentials. Matching conditions with discontinuities of 1st and 2nd kind are specified on the interface. Correct resolution of the singularities is achieved with a “step-doubling” condensing grid. Prototype calculations are reported for the Bessel equation used to choose the condensing grid parameters. The field equations are solved numerically by five-point matrix sweeping with 2×2 matrices. Simulation results are reported for the process of amplification.