On the convergence of a numerical method for a hypersingular integral equation on a closed surface
type: Item
instance of: scholarly article
title: On the convergence of a numerical method for a hypersingular integral equation on a closed surface
zbMATH Open document ID: 1215.65203
DOI: 10.1134/S0012266110090119
author: G. V. Ryzhakov
author: A. V. Setukha
published in: Differential Equations
publication date: 2011-04-01T00:00:00Z
review text: We consider a linear integral equation with a hypersingular integral treated in the sense of the Hadamard finite value. This equation arises in the solution of the Neumann boundary value problem for the Laplace equation with a representation of a solution in the form of a double-layer potential. We consider the case in which the interior or exterior boundary value problem is solved in a domain whose boundary is smooth closed surface, and an integral equation is written out of that surface. For the integral operator in that equation, we suggest quadrature formulas like the method of vortical frames with a regularisation, which provides its approximation on the entire surface for the use of a nonstructured partition. We construct a numerical scheme for the integral equation on the basis of suggested quadrature formulas, prove an estimate for the norm of inverse matrix of related system of linear equations and the uniform convergence of numerical solutions to the exact solution of the hypersingular integral equation on the grid.
reviewed by: Josef Kofroň
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 45A05
zbMATH DE Number: 5873488
zbMATH Keywords: hypersingular integral
zbMATH Keywords: Hadamard finite value
zbMATH Keywords: quadrature formulas
zbMATH Keywords: linear integral equation
zbMATH Keywords: Neumann boundary value problem
zbMATH Keywords: Laplace equation
zbMATH Keywords: double-layer potential
zbMATH Keywords: method of vortical frames
zbMATH Keywords: regularisation
zbMATH Keywords: convergence
MaRDI profile type: Publication
Wikidata QID: Q115252490
cites work: Q4390414
cites work: On the three-dimensional Neumann boundary value problem with a generalized boundary condition in a domain with smooth closed boundary
description: scientific article; zbMATH DE number 5873488