Singularity subtraction in a multidimensional Fredholm integral equation of the second kind with a singular kernel

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216275%3A25530%2F19%3A39915665" target="_blank" >RIV/00216275:25530/19:39915665 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1063/1.5114512" target="_blank" >http://dx.doi.org/10.1063/1.5114512</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.5114512" target="_blank" >10.1063/1.5114512</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Singularity subtraction in a multidimensional Fredholm integral equation of the second kind with a singular kernel

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Singularity subtraction in a multidimensional Fredholm integral equation of the second kind with a singular kernel

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

AIP Conference Proceedings. Vol. 2116

ISBN

978-0-7354-1854-7

ISSN

0094-243X

e-ISSN

—

Počet stran výsledku

4

Strana od-do

1-4

Název nakladatele

American Institute of Physics

Místo vydání

Melville

Místo konání akce

Rhodos

Datum konání akce

13. 9. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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