Analytical Solution of the Three-Dimensional Laplace Equation in Terms of Linear Combinations of Hypergeometric Functions

被引：8

作者：

Lupica, Antonella ^{[1
]}

Cesarano, Clemente ^{[2
]}

Crisanti, Flavio ^{[1
]}

Ishkhanyan, Artur ^{[3
,4
]}

机构：

[1] Univ Tuscia, Dept Econ Engn Soc & Business Org DEIm, I-01100 Viterbo, Italy

[2] Int Telemat Univ Uninettuno, Sect Math, I-00186 Rome, Italy

[3] Russian Armenian Univ, Dept Gen Phys, Yerevan 0051, Armenia

[4] Inst Phys Res, Ashtarak 0203, Armenia

来源：

MATHEMATICS | 2021年 / 9卷 / 24期

关键词：

Laplace equation; Heun equation; analytic solution; cap-cyclide geometry; standard toroidal geometry; hypergeometric functions; MHD-EQUILIBRIA;

D O I：

10.3390/math9243316

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present some solutions of the three-dimensional Laplace equation in terms of linear combinations of generalized hyperogeometric functions in prolate elliptic geometry, which simulates the current tokamak shapes. Such solutions are valid for particular parameter values. The derived solutions are compared with the solutions obtained in the standard toroidal geometry.

引用

页数：16

共 34 条

[1] Simulation of the three-dimensional Laplace equation on an interactive three-dimensional spreadsheet
Lam, CY
INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS IN TECHNOLOGY, 1996, 9 (5-6) : 259 - 271
[2] The Robin problem for the Laplace equation in a three-dimensional starlike domain
Caratelli, D.
Ricci, P. E.
Gielis, J.
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (03) : 713 - 719
[3] Algebras of functionally invariant solutions of the three-dimensional Laplace equation
I. P. Mel'nichenko
Ukrainian Mathematical Journal, 2003, 55 (9) : 1551 - 1559
[4] Solution of a diffusion of dust problem in terms of hypergeometric functions
Kalla, SL
AlZamil, A
MATHEMATICAL AND COMPUTER MODELLING, 1997, 26 (03) : 87 - 93
[5] UNIFORM MEYER SOLUTION TO THE THREE DIMENSIONAL CAUCHY PROBLEM FOR LAPLACE EQUATION
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AnalysisinTheoryandApplications, 2011, 27 (03) : 265 - 277
[6] The Laplace equation in the exterior of the Hankel contour and novel identities for hypergeometric functions
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[7] A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
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[8] A method for solving an exterior three-dimensional boundary value problem for the Laplace equation
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[9] Three-dimensional book data page segmentation and extraction method using Laplace equation
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JOURNAL OF ADVANCED SIMULATION IN SCIENCE AND ENGINEERING, 2021, 8 (02): : 223 - 236
[10] Efficient analytical evaluation of the singular BEM integrals for the three-dimensional Laplace and Stokes equations over polygonal elements
Bohm, Sebastian
Runge, Erich
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2024, 161 : 70 - 77

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