V. S. Eminova - Post-graduate Student, Yaroslav-the-Wise Novgorod State University. E-mail: eminovsi@mail.ru

The integral-differential equation of the circular impedance vibrator antenna with surface boundary conditions of the impedance type has been studied. The original equation is two-dimensional. After highlighting features, we have the one-dimensional integral-differential equation. The main operator of the equation is hypersingular operator. This operator is positive-defined, and its inverse operator is completely continuous. As a result, the original integral-differential equation is equivalent to a Fredholm-s equation of the second kind. To solve the integral-differential equation, a numerical-analytical method is proposed which is based on Chebyshev-s polynomials of the second kind, multiplied by a weighting function. The basis functions satisfy the known Meixner-s conditions on the edge. An important problem of calculating the matrix elements is solved. Numerical result demonstrate the effectiveness of the proposed method.