On the numerical solution of a complete two-dimensional hypersingular integral equation by the method of discrete singularities

DOI10.1134/S0012266113020092zbMath1275.65094WikidataQ115252064 ScholiaQ115252064MaRDI QIDQ1955648

S. G. Lebedeva, Alexey V. Setukha

Publication date: 17 June 2013

Published in: Differential Equations (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical exampleserror estimateHelmholtz equationFredholm alternativemethod of discrete singularitiestwo-dimensional hypersingular integral equationHadamard principle valuequadrature-type numerical methodvon Neumann boundary value problem

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Boundary element methods for boundary value problems involving PDEs (65N38) Linear integral equations (45A05)

Related Items (10)

Convergence of a numerical method for solving a hypersingular integral equation on a segment with the use of piecewise linear approximations on a nonuniform grid ⋮ Convergence of the piecewise linear approximation and collocation method for a hypersingular integral equation on a closed surface ⋮ Method of hypersingular integral equations in a three-dimensional problem of diffraction of electromagnetic waves on a piecewise homogeneous dielectric body ⋮ On the solvability of a complete two-dimensional hypersingular integral equation ⋮ Numerical solution of 3D problems of electromagnetic wave diffraction on a system of ideally conducting surfaces by the method of hypersingular integral equations ⋮ On the solvability of a hypersingular integral equation on a surface with isothermal coordinates ⋮ Method of boundary integral equations with hypersingular integrals in boundary-value problems ⋮ The method of relocation of boundary condition for the problem of electromagnetic wave scattering by perfectly conducting thin objects ⋮ Approximation of Hypersingular Integral Operators With Cauchy Kernel ⋮ Numerical solution of a surface hypersingular integral equation by piecewise linear approximation and collocation methods

Cites Work

• The three-dimensional Neumann problem with generalized boundary conditions and the Prandtl equation
• Construction of fundamental solutions of the Neumann boundary value problem in a domain outside an open plane surface
• Unnamed Item

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