On Fredholm property of hypersingular integral operators in special classes of functions
Известия высших учебных заведений. Поволжский регион: Физико-математические наукиBackground. Hypersingular integral equations on a segment that arise in many issues of mathematical physics are considered. Materials and methods. Hypersingular equations are studied in special classes of functions, which are represented by Fourier ...
Yu.G. Smirnov
doaj +3 more sources
On approximation of hypersingular integral operators by bounded ones
Journal of Mathematical Analysis and Applications, 2022 We solve the Stechkin problem about approximation of generally speaking unbounded hypersingular integral operators by bounded ones. As a part of the proof, we also solve several related and interesting on their own problems. In particular, we obtain sharp Landau-Kolmogorov type inequalities in both additive and multiplicative forms for hypersingular ...
Vladyslav Babenko +2 more
openaire +4 more sources
Approximate Methods for Solving Linear and Nonlinear Hypersingular Integral Equations
Axioms, 2020 We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides.
Ilya Boykov +2 more
doaj +2 more sources
Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2020 We consider fractional Sobolev spaces Hθ(Γ), θ∈[0, 1] on a 2D surface Γ. We show that functions in Hθ(Γ) can be decomposed into contributions with local support in a stable way. Stability of the decomposition is inherited by piecewise polynomial subspaces.
Michael Karkulik +2 more
core +5 more sources
Hypersingular Integral Equations of Prandtl’s Type: Theory, Numerical Methods, and Applications
Axioms, 2022 In this paper, we propose and justify a spline-collocation method with first-order splines for approximate solution of nonlinear hypersingular integral equations of Prandtl’s type.
Ilya Boykov +2 more
doaj +2 more sources
OPERATOR METHOD IN THE PROBLEM OF THE H-POLARIZED WAVE DIFFRACTION BY TWO SEMI-INFINITE GRATINGS PLACED IN THE SAME PLANE [PDF]
Radio Physics and Radio Astronomy, 2021 Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper
M. E. Kaliberda +2 more
doaj +1 more source
Continuous operator method application for direct and inverse scattering problems
Журнал Средневолжского математического общества, 2021 We describe the continuous operator method for solution nonlinear operator equations and discuss its application for investigating direct and inverse scattering problems.
Boykov Ilya V. +3 more
doaj +1 more source
Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks
Mathematics, 2022 A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems.
Ilya Boykov +2 more
doaj +1 more source
SIAM Journal on Numerical Analysis, 2023 This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value problems for elliptic partial differential equations. The quadrature is based on a uniform grid in parameter space coupled with the standard punctured Trapezoidal rule.
Bowei Wu, Per-Gunnar Martinsson
openaire +3 more sources
Bilinear integral operators with certain hypersingularities
Journal of Mathematical Analysis and Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heo, Yaryong +2 more
openaire +1 more source