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An integral equation related to the exterior riemann-hilbert problem on region with corners

Ismail, Munira and Zamzamir, Zamzana and Mohamed Murid, Ali Hassan (2008) An integral equation related to the exterior riemann-hilbert problem on region with corners. Journal of Fundamental Sciences, 4 (2). pp. 369-377. ISSN 1823-626X

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Official URL: http://jfs.ibnusina.utm.my/index.php/jfs/issue/vie...

Abstract

Nasser in 2005 gives the first full method for solving the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral equation. However, his treatment of RH problem does not include regions with corners. Later, Ismail in 2007 provides a numerical solution of the interior RH problem on region with corners via Nasser’s method together with Swarztrauber’s approach, but Ismail does not develop any integral equation related to exterior RH problem on region with corners. In this paper, we introduce a new integral equation related to the exterior RH problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. We obtain a new integral equation that adopts Ismail’s method which does not involve conformal mapping. This result is a generalization of the integral equation developed by Nasser for the exterior RH problem on smooth region. The solvability of the integral equation in accordance with the Fredholm alternative theorem is presented. The proof of the equivalence of our integral equation to the RH problem is also provided

Item Type:Article
Uncontrolled Keywords:Riemann-Hilbert problem, Fredholm integral equation
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:7102
Deposited By: Mohamad Ali Duki
Deposited On:23 Dec 2008 01:58
Last Modified:07 Oct 2010 08:11

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