A. V. Sochilin - Ph.D. (Eng.), Associate Professor, Department of Radiosystems, Institute of electronic and informational systems of Yaroslav, Wise Novgorod State University
I. S. Eminov - Ph.D. (Eng.), Wise Novgorod State University
V. S. Eminova - Post-graduate Student, Department of Informational Technology and Systems, Institute of Electronic and informational Systems of Yaroslav, Wise Novgorod State University

The work is devoted to diffraction of electromagnetic waves on arbitrary curvilinear cylindrical surface. The research is based on the separation of logarithmic singularity in a kernel of integral equation. All that, the operator of problem is represented as the sum of two operators of the main hyper-singular operator and of the completely continuous operator. The hyper-singular operator is positive defined, and the inverse operator is completely continuous. As the result, the original equation is equivalent for second kind equation by Fredholm. For solution of integro-differential equation is proposed the direct numerical method on basis of second kind polynomials by Chebyshev, which were multiplied on a weight function. The matrix of main operator at the basis is found a unitary matrix. Besides basis functions comply with well-known conditions on edge by Meixner. The important problem of calculus of matrix elements is solved. The example of calculation is considered, and effectiveness of the proposed method is demonstrated.