On estimate of the gradient of the hypersingular integral equation solution with use of some numerical scheme

Gleb V. Ryzhakov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The Neumann boundary value problem for the Laplace equation arises in the theoretical aerodynamic. We consider the problem in a domain, whose boundary is a smooth closed surface. One of the methods of solving is to reduce the boundary value problem to the linear hypersingular integral equation written out on the surface under consideration. For the integral operator in that equation, we suggest quadrature formulas like the method of vortical frames with a regularization. The formula provides approximation of the unknown function and it's surface gradient 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. This scheme provides the uniform convergence of numerical solutions to the exact solution of the hypersingular integral equation as well as the uniform convergence of finite difference gradient of numerical solution to the exact gradient of unknown function.

Original languageEnglish
Title of host publication11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
Pages400-403
Number of pages4
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 - Rhodes, Greece
Duration: 21 Sep 201327 Sep 2013

Publication series

NameAIP Conference Proceedings
Volume1558
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013
Country/TerritoryGreece
CityRhodes
Period21/09/1327/09/13

Keywords

  • boundary value problem
  • finite difference gradient
  • singular integral equation
  • vortex method

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