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Approximate methods for solving degenerate singular integral equations
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2023 Background. Singular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has been studied quite well, but as far as the authors know, there are currently no analytical methods ...
Il'ya V. Boykov, Anastasiya A. Pivkina
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Non-homogeneous impulsive time fractional heat conduction equation
Journal of Numerical Analysis and Approximation Theory, 2023 This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations.
Arman Aghili
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On an Integral Equation with the Riemann Function Kernel
Axioms, 2022 This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations ...
Sergei Sitnik, Abdul Ahad Arian
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An explicit kernel-split panel-based Nystr\"om scheme for integral equations on axially symmetric surfaces [PDF]
, 2016 A high-order accurate, explicit kernel-split, panel-based, Fourier-Nystr\"om discretization scheme is developed for integral equations associated with the Helmholtz equation in axially symmetric domains.
Helsing, Johan, Karlsson, Anders
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Singular Volterra integral equations
Applied Mathematics Letters, 2000 The authors study the existence of a nonnegative solution to the Volterra integral equation \[ y(t) = h(t)+ \int_0^t k(t,s)f(s,y(s)) ds,\quad t\in [0,T], \] where the nonlinearity \(f(t,y)\) may be singular at \(y=0\). The assumptions used are such that they easily get a result on the existence of a solution of the singular initial value problem \(y ...
Agarwal, R.P., O'Regan, D.
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TO THE QUESTION OF UNIQUENESS OF DEGENERATE SINGULAR INTEGRAL EQUATIONS SOLUTIONS
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. The work is devoted to the study of sets of functions in which the condition for the unique solvability of degenerate singular integral equations is satisfied.
I. V. Boykov +2 more
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Journal of Inequalities and Applications, 2017 The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities.
Zizun Li, Wu-Sheng Wang
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Boosting the Maxwell double layer potential using a right spin factor [PDF]
, 2018 We construct new spin singular integral equations for solving scattering problems for Maxwell's equations, both against perfect conductors and in media with piecewise constant permittivity, permeability and conductivity, improving and extending earlier ...
Rosén, Andreas
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AN APPROXIMATE METHODS FOR SOLVING POLYSINGULAR INTEGRAL EQUATIONS IN DEGENERATE CASES
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. This work is devoted to the study of sets of functions in which the condition of unique solvability of degenerate polysingular integral equations is satisfied, and to the construction of approximate methods for solving polysingular integral
I. V. Boykov +2 more
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H-polarized plane wave scattering by graphene strip grating on top of a dielectric substrate
Вісник Харківського національногоуніверситету імені В.Н. Каразіна. Серія: Радіофізика та електроніка, 2022 Relevance. Graphene is relatively new material which properties can be controlled dynamically under external influence by applying electrostatic or magnetostatic field. Also graphene can absorb electromagnetic field. Graphene strips with substrate can be
M.E. Kaliberda, S. A. Pogarsky
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