Solving Robin problems in multiply connected regions via an integral equation with the generalized Neumann kernel

被引：1

作者：

Al-Shatri, Shwan H. H. ^{[1
]}

Murid, Ali H. M. ^{[1
,2
]}

Ismail, Munira ^{[1
]}

Muminov, Mukhiddin I. ^{[1
]}

机构：

[1] Univ Teknol Malaysia, Dept Math Sci, Fac Sci, Johor Baharu 81310, Johor, Malaysia

[2] Univ Teknol Malaysia, UTM Ctr Ind & Appl Math UTM CIAM, Ibnu Sina Inst Sci & Ind Res, Johor Baharu 81310, Johor, Malaysia

来源：

BOUNDARY VALUE PROBLEMS | 2016年

关键词：

Robin problem; Riemann-Hilbert problem; integral equation; generalized Neumann kernel; multiply connected region; RIEMANN-HILBERT PROBLEM; BOUNDARY;

D O I：

10.1186/s13661-016-0599-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a boundary integral equation method for finding the solution of Robin problems in bounded and unbounded multiply connected regions. The Robin problems are formulated as Riemann-Hilbert problems which lead to systems of integral equations and the related differential equations are also constructed that give rise to unique solutions, which are shown. Numerical results on several test regions are presented to illustrate that the approximate solution when using this method for the Robin problems when the boundaries are sufficiently smooth are accurate.

引用

页数：23

共 50 条

[1] Solving Robin problems in multiply connected regions via an integral equation with the generalized Neumann kernel
Shwan HH Al-Shatri
Ali HM Murid
Munira Ismail
Mukhiddin I Muminov
Boundary Value Problems, 2016
[2] Solving Robin Problems in Bounded Doubly Connected Regions via an Integral Equation with the Generalized Neumann Kernel
Al-Shatri, Shwan H. H.
Murid, Ali H. M.
Ismail, Munira
ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS, 2016, 1750
[3] Solving a class of Robin problems in simply connected regions via integral equations with a generalized Neumann kernel
Al-Shatri, Shwan H. H.
Murid, Ali H. M.
Ismail, Munira
SCIENCEASIA, 2017, 43 : 69 - 78
[4] Solving a Mixed Boundary Value Problem via an Integral Equation with Adjoint Generalized Neumann Kernel in Bounded Multiply Connected Regions
Al-Hatemi, Samer A. A.
Murid, Ali H. M.
Nasser, Mohamed M. S.
PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM20): RESEARCH IN MATHEMATICAL SCIENCES: A CATALYST FOR CREATIVITY AND INNOVATION, PTS A AND B, 2013, 1522 : 508 - 517
[5] Boundary integral equations with the generalized Neumann kernel for Laplace's equation in multiply connected regions
Nasser, M. M. S.
Murid, A. H. M.
Ismail, M.
Alejaily, E. M. A.
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (09) : 4710 - 4727
[6] Solving a Mixed Boundary Value Problem via an Integral Equation with Generalized Neumann Kernel on Unbounded Multiply Connected Region
Alhatemi, S. A. A.
Murid, A. H. M.
Nasser, M. M. S.
MALAYSIAN JOURNAL OF FUNDAMENTAL AND APPLIED SCIENCES, 2012, 8 (04): : 193 - 197
[7] A boundary integral equation with the generalized Neumann kernel for a mixed boundary value problem in unbounded multiply connected regions
Al-Hatemi, Samer A. A.
Murid, Ali H. M.
Nasser, Mohamed M. S.
BOUNDARY VALUE PROBLEMS, 2013, : 1 - 17
[8] A boundary integral equation with the generalized Neumann kernel for a mixed boundary value problem in unbounded multiply connected regions
Samer AA Al-Hatemi
Ali HM Murid
Mohamed MS Nasser
Boundary Value Problems, 2013
[9] Integral Equation Approach for Computing Green's Function on Doubly Connected Regions via the Generalized Neumann Kernel
Aspon, Siti Zulaiha
Murid, Ali Hassan Mohamed
Nasser, Mohamed M. S.
Rahmat, Hamisan
JURNAL TEKNOLOGI, 2014, 71 (01):
[10] Computing Green's Function on Unbounded Doubly Connected Regions via Integral Equation with the Generalized Neumann Kernel
Aspon, Siti Zulaiha
Murid, Ali Hassan Mohamed
Rahmat, Hamisan
PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): GERMINATION OF MATHEMATICAL SCIENCES EDUCATION AND RESEARCH TOWARDS GLOBAL SUSTAINABILITY, 2014, 1605 : 215 - 220

← 1 2 3 4 5 →