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Gandel, Yu. V., “Boundary-Value Problems for the Helmholtz Equation and their Discrete Mathematical Models,” Journal of Mathematical Sciences, 171(1), 74-88, 2010.

has been cited by the following article:

Article

The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice

1Department of Mathematical Physics and Computational Mathematics, Karazin Kharkiv National University, Kharkiv, Ukraine

2Department of Fundamental Science, National Academy of NGU, Kharkiv, Ukraine


American Journal of Applied Mathematics and Statistics. 2014, Vol. 2 No. 6, 369-375
DOI: 10.12691/ajams-2-6-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
Gandel Yu. V., Dushkin V.D.. The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice. American Journal of Applied Mathematics and Statistics. 2014; 2(6):369-375. doi: 10.12691/ajams-2-6-3.

Correspondence to: Dushkin  V.D., Department of Fundamental Science, National Academy of NGU, Kharkiv, Ukraine. Email: dushkinvd@gmail.com

Abstract

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.

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