Computing Robin Problem on Unbounded Simply Connected Regions via an Integral Equations with the Generalized Neumann Kernel

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Shwan H. H. Al-Shatri Karzan Wakil Munira Ismail

Abstract

This paper presents a new boundary integral equation method for the solution of unbounded Robin problems in simply connected region. We show how to reformulate the Robin problem as Riemann-Hilbert problems which lead to system of integral equations, 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 the solution technique for the Robin problem when the boundaries are sufficiently smooth.

Keywords

Robin problem, Riemann-Hilbert problem, Integral equation, Generalized Neumann kernel, Simply connected region.

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