The justification of the numerical solution of the wave scattering problem on shield impedance lattice
Keywords:
impedance structures, existence of approximate solution, the rate of convergence of the approximate solutions
Abstract
The method for numerical solution of boundary singular integral equations of the problems of waves scattering of on shield impedance lattice had been discussed. The convergence of the approximate solutions to the exact solution had been proved. The rate of convergence of this process had been found.Downloads
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References
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Yu. V. Gandel, V. D. Dushkin Mathematical Model of Scattering of Polarized Waves on Impedance Strips Located on a Screened Dielectric Layer // Journal of Mathematical Sciences, 2016, Springer US. - pp. 156-166
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Yu. V. Gandel’, V.D. Dushkin Mathematical model of polarized wave scattering on impedance strips located on screened dielectric layer // Мат. методи та фіз.-мех. поля, 2014. – 57, №1. –с. 125-132
Yu. V. Gandel, V. D. Dushkin Mathematical Model of Scattering of Polarized Waves on Impedance Strips Located on a Screened Dielectric Layer // Journal of Mathematical Sciences, 2016, Springer US. - pp. 156-166
N. I. Akhiezer, Lectures on integral transforms. Translations of Mathematical Monographs, 70. American Mathematical Society, Providence, RI, 1988.
Yu.V. Gandel', Parametric representations of integral and psevdodifferential operators in diffraction problems. – Conf. Proc., 10th Int.Conf. on Math. Methods in Electromagnetic Theory. (Dnepropetrovsk, Ukraine, Sept. 14-17), Dnepropetrovsk, 2004. 57 - 62.
Yu. V. Gandel’, Boundary-Value Problems for the Helmholtz Equation and their Discrete Mathematical Models. – Journal of Mathematical Sciences. 171 (2010). No. 1, 74-88.
Y.V. Gandel and V.D. Dushkin, The method of parametric representations of integral and pseudo-differential operators in diffraction problems on electrodynamic structures. – Proceedings of the International Conference Days on Diffraction DD 2012 (28 May-1 June 2012), St. Petersburg, 2012, 76-81.
V.D. Dushkin The Justification of Numerical Solution of Boundary Integral Equations of Wave Scattering Problems on Impedance Lattice / Душкин В. Д. // Вестник Харк. нац. ун-та., – 2014. – № 1120. Сер. "Математика, прикладная математика и механика", вып. 69. – С. 20-28
Gandel Yu., and 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, Science and Education Publishing, 2.6 (2014): 369-375.
Гандель Ю. В., Душкин В. Д. Математические модели двумерных задач дифракции: Сингулярные интегральные уравнения и численные методы дискретных особенностей [Текст]: монография. – Х. : Акад. ВВ МВД Украины, 2012. –544с.
Гандель Ю.В. Лекции о численных методах для сингулярных интегральных уравнений. Введение в методы вычисления сингулярных и гиперсингулярных интегралов. — Х: Издательство Харьковского национального университета, 2001. — 92 с.
Kutateladze S.S. Fundamentals of Functional Analysis . — Dordrecht, the Netherlands: Kluwer Academic Publishers Group, 1996. — 277 p.
I.P. Natanson, Constructive Function Theory, Volume 1, Frederic Ungar Puplishing Co., New York, 1964. 232р.
Габдулхаев, Б. Г. Оптимальные аппроксимации решений линейных задач. – Казань: Изд-во Казан. ун-та. – 1980. – 232 с.
Published
2017-05-27
How to Cite
Гандель, Ю. В., & Душкин, В. Д. (2017). The justification of the numerical solution of the wave scattering problem on shield impedance lattice. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 32, 15-24. Retrieved from https://periodicals.karazin.ua/mia/article/view/8575
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