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

• Main Authors: Al-Shatri, S. H. H., Murid, A. H. M., Ismail, M., Muminov, M. I.
• Format: Article
• Language: English
• Published: Springer International Publishing 2016
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/71868/1/AliHassanMohamed2016_SolvingRobinProblemsinMultiplyConnected.pdf; http://eprints.utm.my/id/eprint/71868/; https://www.scopus.com/inward/record.uri?eid=2-s2.0-84966262709&doi=10.1186%2fs13661-016-0599-2&partnerID=40&md5=e3a7cb835389aa34abb4b8210d04d0db

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.