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A 2D problem of E-polarized wave radiation from an infinite array of stepped horns with dielectric elements passing through the horns and protruding above the horn apertures is considered. A hybrid projection method of solution reducing the problem to a system of ordinary differential equations for variable coefficients of the field expansion is proposed. The differential equations are subsequently reduced to linear algebraic equations after applying the one-dimensional method of finite elements. The solution of the algebraic system is used for calculation of the array reflection coefficient and element pattern. Some new numerical results characterizing both the method itself and the capabilities of the horn-dielectric arrays are presented and discussed.