Standard

Approximate methods for solving linear and nonlinear hypersingular integral equations. / Boykov, Ilya; Roudnev, Vladimir; Boykova, Alla.

в: Axioms, Том 9, № 3, 74, 01.09.2020.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Boykov, I, Roudnev, V & Boykova, A 2020, 'Approximate methods for solving linear and nonlinear hypersingular integral equations', Axioms, Том. 9, № 3, 74. https://doi.org/10.3390/AXIOMS9030074

APA

Boykov, I., Roudnev, V., & Boykova, A. (2020). Approximate methods for solving linear and nonlinear hypersingular integral equations. Axioms, 9(3), [74]. https://doi.org/10.3390/AXIOMS9030074

Vancouver

Boykov I, Roudnev V, Boykova A. Approximate methods for solving linear and nonlinear hypersingular integral equations. Axioms. 2020 Сент. 1;9(3). 74. https://doi.org/10.3390/AXIOMS9030074

Author

Boykov, Ilya ; Roudnev, Vladimir ; Boykova, Alla. / Approximate methods for solving linear and nonlinear hypersingular integral equations. в: Axioms. 2020 ; Том 9, № 3.

BibTeX

@article{bc7e1699f8774107a7eb54e2d378a9e3,
title = "Approximate methods for solving linear and nonlinear hypersingular integral equations",
abstract = "We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method.",
keywords = "Hypersingular integral equations, Iterative projection method, Lyapunov stability theory",
author = "Ilya Boykov and Vladimir Roudnev and Alla Boykova",
note = "Publisher Copyright: {\textcopyright} 2020 by the authors.",
year = "2020",
month = sep,
day = "1",
doi = "10.3390/AXIOMS9030074",
language = "English",
volume = "9",
journal = "Axioms",
issn = "2075-1680",
publisher = "MDPI AG",
number = "3",

}

RIS

TY - JOUR

T1 - Approximate methods for solving linear and nonlinear hypersingular integral equations

AU - Boykov, Ilya

AU - Roudnev, Vladimir

AU - Boykova, Alla

N1 - Publisher Copyright: © 2020 by the authors.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method.

AB - We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method.

KW - Hypersingular integral equations

KW - Iterative projection method

KW - Lyapunov stability theory

UR - http://www.scopus.com/inward/record.url?scp=85088385672&partnerID=8YFLogxK

U2 - 10.3390/AXIOMS9030074

DO - 10.3390/AXIOMS9030074

M3 - Article

AN - SCOPUS:85088385672

VL - 9

JO - Axioms

JF - Axioms

SN - 2075-1680

IS - 3

M1 - 74

ER -

ID: 88225162