Method of integral summation identities in the problem of a TE-polarized electromagnetic wave diffraction on a vertical barrier in an infinite waveguide

In this paper the boundary value problem (BVP) for the Helmholtz equation associated with the diffraction of a TE-polarized electromagnetic wave on a vertical harrier in an infinite waveguide is investigated. Using the partial domain method the BVP is reduced to an infinite system of linear algebraic equations of the second kind (ISLAE-2). The equivalence of the initial BVP and the ISLAE-2 and the Fredholm property of the matrix operator of ISLAE-2 in the weighted Hilbert space of infinite sequences that ensures the fulfillment of energy (edge) condition are proved. The truncation (reduction) method is developed on the basis of semi-regularization for the approximate solution of ISLAE-2. Broad series of computational experiments are performed.