Approximate Solving of the Third Boundary
Value Problems for Helmholtz Equations in
the Plane with Parallel Cuts

V.D. Dushkin

National Academy of the National Guard of Ukraine 3 Zakhystnykiv Ukrainy Sq., Kharkiv, 61001, Ukraine
E-mail: dushkinvd@gmail.com

Received October 10, 2015, revised February 6, 2017

Abstract

In the paper, the method of approximate solution of boundary integral equations of the original problem is proposed. The systems of boundary integral equations of the problem are obtained by the method of parametric representation of integral transforms. The convergence of approximate
solutions to the exact solution of the original problem is guaranteed by the
propositions proved in the paper. Also, the rate of convergence of approximate
solutions to exact solutions is found.

Mathematics Subject Classification 2000: 45P05, 45L05. Key words: approximate solution of boundary integral equations, singular
integral equation, existence of approximate solution, rate of convergence of approximate solution.