Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures

Samokhin, A. B.; Samokhina, A. S.; Yurchenkov, I. A.

doi:10.31857/S0374064123090108

PII

10.31857/S0374064123090108-1

DOI

10.31857/S0374064123090108

Publication type

Article

Status

Published

Authors

A. B. Samokhin

Affiliation: MIREA—Russian Technological University, Moscow, 119454, Russia

A. S. Samokhina

Affiliation: Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

I. A. Yurchenkov

Affiliation: MIREA—Russian Technological University, Moscow, 119454, Russia

Volume/ Edition

Volume 59 / Issue number 9

Pages

1260-1265

Abstract

We consider the differential and integral statements of problems of acoustic scattering by three-dimensional bounded transparent structures described by an integral equation. The results of the numerical solution of the integral equation describing the class of problems under consideration are presented. A theorem on existence and uniqueness of the solution is proved.

Keywords

Date of publication

18.09.2025

Year of publication

2025

Number of purchasers

Views

References

1. Колтон Д., Кресс Р. Методы интегральных уравнений в теории рассеяния. М., 1990.
2. Кошляков Н.С., Глинер Э.Б., Смирнов M.M. Уравнения в частных производных математической физики. М., 1970.
3. Хермандер Л. Анализ линейных дифференциальных уравнений с частичными производными. M., 1986.
4. Самохин А.Б. Методы и эффективные алгоритмы решения многомерных интегральных уравнений // Russ. Technological J. 2022. V. 10. № 6. P. 70-77.
5. Vainikko G. Multidimensional Weakly Singular Integral Equations. Heidelberg, 1993.
6. Самохин A.Б., Самохина А.С., Скляр А.С., Шестопалов Ю.В. Итерационные методы градиентного спуска для решения линейных уравнений // Журн. вычислит. математики и мат. физики. 2019. T. 59. № 8. C. 1331-1339.
7. Henk A., van der Vorst. Iterative Krylov Methods for Large Linear System. Cambridge, 2003.
8. Самохин А.Б. Объёмные сингулярные интегральные уравнения электродинамики М., 2021.

GOST	Samokhin A., Samokhina A., Yurchenkov I. Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures // Differential Equations. – 2023. – V. 59. – Issue number 9 C. 1260-1265 . URL: https://differeqras.ru/10-31857-s0374064123090108-1/?version_id=112331. DOI: 10.31857/S0374064123090108
MLA	Samokhin, A. B, Samokhina, A. S, Yurchenkov, I. A "Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures." Differential Equations. 59.9 (2023).:1260-1265. DOI: 10.31857/S0374064123090108
APA	Samokhin A., Samokhina A., Yurchenkov I. (2023). Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures. Differential Equations. vol. 59, no. 9, pp.1260-1265 DOI: 10.31857/S0374064123090108

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Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures

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RAS MathematicsДифференциальные уравнения Differential Equations

Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures

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