eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2333-4576 2014-11-19 2 6 369 375 10.12691/ajams-2-6-3 AJAMS2014263 article Gandel Yu. V. 1 Dushkin V.D. dushkinvd@gmail.com 2 Department of Mathematical Physics and Computational Mathematics, Karazin Kharkiv National University, Kharkiv, Ukraine Department of Fundamental Science, National Academy of NGU, Kharkiv, Ukraine In this article the method for numerical solution of boundary integral equations of the original problem is proposed. This method is one of the modifications of Nystrom-type methods; particularly the method of discrete vortices. The convergence of the numerical solutions to the exact solution of the problem is guaranteed by propositions proved in this article. Also, the rate of convergence of the approximate solutions to the exact solution had been found. http://pubs.sciepub.com/ajams/2/6/3/ajams-2-6-3.pdf singular integral equation modification of method of discrete vortices existence of approximate solution the rate of convergence of the approximate solutions