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

Shwan Hussein Alshatri | Zendy; Karzan Wakil | Zendy; Munira Ismail | Zendy

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

Author(s) -

Shwan Hussein Alshatri,

Karzan Wakil,

Munira Ismail

Publication year - 2017

Publication title -

kurdistan journal of applied research

Language(s) - English

Resource type - Journals

eISSN - 2411-7706

pISSN - 2411-7684

DOI - 10.24017/science.2017.3.10

Subject(s) - mathematics , robin boundary condition , boundary value problem , integral equation , neumann boundary condition , domain (mathematical analysis) , mathematical analysis , mixed boundary condition , dirichlet distribution , kernel (algebra) , free boundary problem , riemann–hilbert problem , partial differential equation , discrete mathematics

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 Nystrom method NM with the trapezoidal rule TR are presented to clarify the solution technique for the Robin problem when the boundaries are sufficiently smooth.

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