THE SOLUTION OF A MIXED BOUNDARY VALUE PROBLEM FOR THE LAPLACE EQUATION IN A MULTIPLY CONNECTED DOMAIN

被引：2

作者：

Ivanshin, P. N. ^{[1
]}

Shirokova, E. A. ^{[1
]}

机构：

[1] Kazan Fed Univ, 18 Kremlyovskaya Str, Kazan 420008, Russia

来源：

PROBLEMY ANALIZA-ISSUES OF ANALYSIS | 2019年 / 8卷 / 02期

关键词：

Cauchy integral; Laplace equation; mixed boundary value problem; multiply connected domain; approximate solution;

D O I：

10.15393/j3.art.2019.5570

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here we apply the Cauchy integral method for the Laplace equation in multiply connected domains when the data on each boundary component has the form of the Dirichlet condition or the form of the Neumann condition. This analytic method gives highly accurate results. We give examples of applications of the method.

引用

页码：51 / 66

页数：16

共 22 条

[1]

Achieser N. I., 1956, Theory of Approximation

[2] UNIFORMLY CONVERGENT APPROXIMATE SOLUTIONS OF FREDHOLM INTEGRAL EQUATIONS [J].

ANSELONE, PM ;

GONZALEZ.JM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1965, 10 (03) :519-&

[3]

Anselone PM., 1964, J MATH ANAL APPL, V9, P268, DOI DOI 10.1016/0022-247X(64)90042-3

[4]

Asmar N. H., 2016, Partial Differential Equations with Fourier Series and Boundary Value Problems

[5]

Axelsson O., 1984, FINITE ELEMENT SOLUT

[6] Galerkin finite element approximations of stochastic elliptic partial differential equations [J].

Babuska, I ;

Tempone, R ;

Zouraris, GE .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2004, 42 (02) :800-825

[7]

Buckner H., 1962, SURVEY NUMERICAL ANA

[8]

Ciarlet PG., 1987, FINITE ELEMENT METHO

[9] Converging Expansions for Lipschitz Self-Similar Perforations of a Plane Sector [J].

Costabel, Martin ;

Riva, Matteo Dalla ;

Dauge, Monique ;

Musolino, Paolo .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2017, 88 (03) :401-449

[10]

Gakhov F.D., 1990, Boundary Value Problems

← 1 2 3 →