Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study

Obaiys, Suzan Jabbar; Ibrahim, Rabha W.; Ahmad, Ahmad F.

doi:10.1007/978-3-030-27407-8_25

Cited by 6 publications

(4 citation statements)

References 39 publications

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“…Theoretical approaches are closely related to the theory of pseudodifferential operators [33][34][35]122]. The reader who is interested in these questions can be recommended literature [122][123][124][125].…”

Section: Discussionmentioning

confidence: 99%

Volumetric integro-differential equations in diffraction and eigenvalue problems (r e v i e w)

Давидович

2022

Optics and Spectroscopy

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Volumetric integral and integro-differential equations are considered that describe problems of diffraction by three-dimensional bodies with given macroscopic permittivity and magnetic permeability, as well as problems on free vibrations of such bodies. Similar equations are obtained for waveguide structures: hollow shielded waveguides with dielectric filling, dielectric waveguides (optical beamguides), photonic-crystal waveguides. Dominantly stationary linear electromagnetic problems are considered. Non-stationary and nonlinear problems are mentioned casually. Numerical results are given for oscillations H01delta and H011 of a cylindrical dielectric resonator, for waves of a rectangular dielectric waveguide and a plasmonic waveguide, dispersion in a photonic crystal, and diffraction by a rectangular dielectric cylinder. Keywords: ...

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Section: Discussionmentioning

confidence: 99%

Volumetric integro-differential equations in diffraction and eigenvalue problems (r e v i e w)

Давидович

2022

Optics and Spectroscopy

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“…Теоретические подходы тесно связаны с теорией псевдодифференциальных операторов [33][34][35]122]. Интересующемуся этими вопросами читателю можно рекомендовать литературу [122][123][124][125].…”

Section: заключениеunclassified

Объемные Интегродифференциальные Уравнения В Задачах Дифракции И В Задачах О Собственных Значениях (О Б З О Р)

Давидович¹

2022

Оптика И Спектроскопия

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Рассмотрены объемные интегральные и интегродифференциальные уравнения, описывающие задачи дифракции на трехмерных телах с заданными макроскопическими диэлектрической и магнитной проницаемостями, а также задачи о свободных колебаниях таких тел. Получены аналогичные уравнения для волноведущих структур: полых экранированных волноводов с диэлектрическим заполнением, диэлектрических волноводов (оптических лучеводов), фотонно-кристаллических волноводов. В основном рассмотрены стационарные линейные электромагнитные задачи. Нестационарные и нелинейные задачи упомянуты вскользь. Приведены численные результаты для колебаний H01delta и H011 цилиндрического диэлектрического резонатора, для волн прямоугольного диэлектрического волновода и плазмонного волновода, дисперсии в фотонном кристалле, дифракции на прямоугольном диэлектрическом цилиндре. Ключевые слова: ...

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“…To find the coefficients b k rewrite Eq. ( 14 where Second integral in (27), can be easily integrated For the first integral in (27) we applied Hasegawa [9] approach, as well as used ( 14)-( 15) to yield where coefficients b k are defined by (25).…”

Section: Construction Of Aqs For Cauchy Type Singular Integralsmentioning

confidence: 99%

Automatic Quadrature Scheme for Cauchy Type Singular Integral on the Variable Interval

Eshkuvatov

AL-HADI

BAHRAMOV

2022

JMSI

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In this note, we consider the product indefinite integral of the form An automatic quadrature scheme (AQS) is constructed for evaluating Cauchy principal singular integrals in two cases. In the first case c∈ [y,z] ⊂ [-1,1] where -1 < y < z < 1, density function h(t) is approximated by the truncated sum of Chebyshev polynomials of the first kind. Direct substitution does not give solutions so we have used the AQS and reduced problems into algebraic equation with unknown parameters bk which can be found in terms of the singular point with some front conditions. In the second case c ∈ [-1,1], the application of the AQS reduced the number of calculations twice and accuracy is increased. As a theoretical result, the convergence theorem of the proposed method is proven in a Hilbert space. Numerical examples with exact solutions and comparisons with other methods are also given, and they are in the line with theoretical findings.

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Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study

Cited by 6 publications

References 39 publications

Volumetric integro-differential equations in diffraction and eigenvalue problems (r e v i e w)

Volumetric integro-differential equations in diffraction and eigenvalue problems (r e v i e w)

Объемные Интегродифференциальные Уравнения В Задачах Дифракции И В Задачах О Собственных Значениях (О Б З О Р)

Automatic Quadrature Scheme for Cauchy Type Singular Integral on the Variable Interval

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