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Volume 43S Number 1 Volume 43 Number 1

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Research articles

ScienceAsia 43S(2017): 69-78 |doi: 10.2306/scienceasia1513-1874.2017.43S.069

Solving a class of Robin problems in simply connected regions via integral equations with a generalized Neumann kernel

Shwan˙H.H.˙Al-Shatria, Ali˙H.M.˙Murida,b,*, Munira˙Ismaila

ABSTRACT:     This paper presents a new boundary integral equation method for the solution of a class of Robin problems in bounded and unbounded simply connected regions. We show how to reformulate the Robin problems as Riemann-Hilbert problems which lead to systems of integral equations, related differential equations, and normalizing conditions that give rise to unique solutions. Numerical results on several test regions are presented to illustrate the solution technique for the Robin problems when the boundaries are sufficiently smooth.

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a Department˙of˙Mathematical˙Sciences, Faculty˙of˙Science, Universiti˙Teknologi˙Malaysia, Johor, Malaysia
b UTM Centre for industrial and Applied Mathematics, Ibnu˙Sina˙Institute˙for˙Scientific˙and˙Industrial˙Research, Universiti˙Teknologi˙Malaysia, Johor, Malaysia

* Corresponding author, E-mail: alihassan@utm.my

Received 22 Aug 2017, Accepted 21 May 2017