Singularity subtraction in a multidimensional Fredholm integral equation of the second kind with a singular kernel
Konferenční objektOtevřený přístuppeer-reviewedpostprintDatum publikování
2019
Autoři
Vedoucí práce
Oponent
Název časopisu
Název svazku
Vydavatel
American Institute of Physics
Abstrakt
A numerical solution of the Fredholm integral equations can be obtained by many methods. Most of them lead to a solution of a system of linear equations with fully populated matrices. In the case of collocation or product integration methods, each element of the matrix is an integral, which needs to be calculated. It causes high computing time in multidimensional problems. Computing time can be reduced by the Nyström method. It is based on substitution of the integral by a numerical integration rule. It has the advantage that only diagonal elements of the matrix are integrals. When the kernel function is singular, a singularity subtraction is needed. However it can not be used for every kernel function and every integration rule. The main point of this paper is the convergence conditions of the Nyström method as applied to a special multidimensional integral equation. The paper includes an illustrative example.
Rozsah stran
p. 1-4
ISSN
0094-243X
Trvalý odkaz na tento záznam
Projekt
Zdrojový dokument
AIP Conference Proceedings. Vol. 2116
Vydavatelská verze
https://aip.scitation.org/doi/abs/10.1063/1.5114512
Přístup k e-verzi
open access
Název akce
International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 (13.09.2018 - 18.09.2018, Rhodos)
ISBN
978-0-7354-1854-7
Studijní obor
Studijní program
Signatura tištěné verze
Umístění tištěné verze
Přístup k tištěné verzi
Klíčová slova
multidimensional integral equations, singularity subtraction, singular kernel, Vícerozměrná integrální rovnice, odstranění singularity, singulární jádro