A. V. Sochilin, I. S. Eminov, S. I. Eminov

There are a lot of works about problem of antenna's synthesis. But many questions have no solutions up to the present. The problem of surface current's calculation for boundary conditions on edge by Meixner isn't solved. For solution of the problem, authors suggested new equation of synthesis of current's on open-ended surface. This work is devoted to adaptation it equations for linear antenna's. The main equation of synthesis of linear antennas is hipersingular equation with small parameter. Algorithm of the solution has been worked out, the complex of programs has been made up, the numerical experiment has been conducted. We'd like to mention, that problems of convergence of numerical methods for solution of integral equations with small parameter were researched not enough. But at the same time, this question is very important. Results for the problem's research will determine, how much often we can put them into practice. This work demonstrating good results of method by Galerkin for calculation of integral equations. The basis function are one's considering boundary conditions on edge by Meixner. Also, we publish the analysis of numerical results.