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New mathematical models for the electric field in a rectangular waveguide, with air filling, are obtained taking account of the nonlinearity of the medium. The models are described by elliptic type partial differential equations. On the basis of a finite difference method, the effective values are determined for the intensity of the electric field in a rectangular waveguide, with air filling, for E-type and H-type waves. The calculation and experimental results are compared, and the error does not exceed 5%.

finite difference method; analysis of electric fields; rectangular waveguide; microwave elements