A Cauchy integral method of the solution of the 2D Dirichlet problem for simply or doubly connected domains

被引：4

作者：

Shirokova, Elena A. ^{[1
]}

El-Shenawy, Atallah ^{[1
]}

机构：

[1] Kazan Fed Univ, Lobachevsky Inst Math & Mech, Kazan, Russia

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 34卷 / 06期

关键词：

Cauchy integral; Dirichlet problem; doubly connected domain; Fredholm integral equation; Fourier polynomial; simply connected domain; POTENTIAL-THEORY; EQUATION METHODS;

D O I：

10.1002/num.22290

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we propose a new method for solving the 2D Laplace equation with Dirichlet boundary conditions in simply and doubly connected domains. Here, we apply the numerical algorithm based on truncated Fourier series and reduce the corresponding Fredholm integral equation to a finite system of linear equations.

引用

页码：2267 / 2278

页数：12

共 50 条

[1] The Approximate Solution of 2D Dirichlet Problem in Doubly Connected Domains
El-shenawy, Atallah
Shirokova, Elena A.
ADVANCES IN MATHEMATICAL PHYSICS, 2018, 2018
[2] A CAUCHY INTEGRAL METHOD TO SOLVE THE 2D DIRICHLET AND NEUMANN PROBLEMS FOR IRREGULAR SIMPLY-CONNECTED DOMAINS
El-Shenawy, A.
Shirokova, E. A.
UCHENYE ZAPISKI KAZANSKOGO UNIVERSITETA-SERIYA FIZIKO-MATEMATICHESKIE NAUKI, 2018, 160 (04): : 778 - 787
[3] Cauchy Problem for the Laplace Equation in 2D and 3D Doubly Connected Domains
Liu, Ji-Chuan
Zhang, Quan-Guo
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2013, 93 (03): : 203 - 219
[4] A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane
Markowsky, Greg
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 464 (02) : 1143 - 1146
[5] Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation
Wei, T.
Qin, H. H.
Shi, R.
INVERSE PROBLEMS, 2008, 24 (03)
[6] ON CAUCHY PROBLEM SOLUTION FOR A HARMONIC FUNCTION IN A SIMPLY CONNECTED DOMAIN
Shirokova, E. A.
Ivanshin, P. N.
PROBLEMY ANALIZA-ISSUES OF ANALYSIS, 2023, 12 (02): : 87 - 96
[7] SOLUTION TO CAUCHY-PROBLEM FOR LAPLACE EQUATION IN A DOUBLY CONNECTED DOMAIN
VABISHCHEVICH, PN
DOKLADY AKADEMII NAUK SSSR, 1978, 241 (06): : 1257 - 1260
[8] A numerical solution of the Dirichlet problem on some special doubly connected regions
Dont M.
Dontová E.
Applications of Mathematics, 1998, 43 (1) : 53 - 76
[9] On the use of an integral equation approach for the numerical solution of a Cauchy problem for Laplace equation in a doubly connected planar domain
Chapko, Roman
Johansson, B. Tomas
Savka, Yuriy
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2014, 22 (01) : 130 - 149
[10] Fourier Solution of the 2D Dirichlet Problem for the Helmholtz Equation
Caratelli, D.
Natalini, P.
Ricci, P. E.
PIERS 2009 MOSCOW VOLS I AND II, PROCEEDINGS, 2009, : 128 - +

← 1 2 3 4 5 →