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

Boundary value problems

Shwan HH Al-Shatri¹  Ali HM Murid¹  Mukhiddin I Muminov¹  Munira Ismail² 

[1] Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor, Malaysia;UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu Sina Institute for Scientific and Industrial Research, University Teknologi Malaysia, Johor, Malaysia

关键词: Robin problem;    Riemann-Hilbert problem;    integral equation;    generalized Neumann kernel;    multiply connected region;   

DOI  :  10.1186/s13661-016-0599-2

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY