Computing Robin Problem on Unbounded Simply Connected Domain via an Integral Equation with the Generalized Neumann Kernel

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

doi:10.24017/science.2017.3.10

Authors

Shwan H. H. Al-Shatri Science Department, Institute of Training and Educational Development in Sualiamni-Iraq Author
Karzan Wakil Sualimani Polytechnic University-Iraq, University of Human Development-Iraq Author
Munira Ismail Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Malaysia Author

DOI:

https://doi.org/10.24017/science.2017.3.10

Keywords:

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

Abstract

A Robin problem is a mixed problem with a linear combination of Dirichlet and Neumann D-N conditions. The aim of this paper are presents a new boundary integral equation BIE method for the solution of unbounded Robin boundary value problem BVP in the simply connected domain. The method show how to reformulate the Robin boundary value problem BVP as Riemann-Hilbert problem RHP which lead to the system of integral equation, and the related differential equations are also created that give rise to unique solutions. Numerical results on several tests regions by the Nyström method NM with the trapezoidal rule TR are presented to clarify the solution technique for the Robin problem when the boundaries are sufficiently smooth.