An integral equation approach for the numerical solution of the Riemann problem on a simply connected region with corners. (13th February 2006)

• Record Type: Journal Article
• Authors: Ismail, Munira; Murid, Ali Hassan Mohd.; Sanugi, Bahrom B.
• Is Part Of: International journal of simulation and process modelling. Volume 2:Number 1/2(2006)
• Page Start: 25
• Page End: 32
• Publication Date: 2006-02-13
• Subjects: integral equation -- Riemann problem -- Dirichlet problem -- boundary with corners -- Picard iteration method -- boundary value problems -- analytic functions; Management -- Computer simulation -- Periodicals; Mathematical models -- Periodicals; Operations research -- Periodicals; Simulation methods -- Periodicals; 003.05
• Languages: English
• ISSNs: 1740-2123

Abstract

In this paper we introduce a new integral equation for computing the numerical solution of the Riemann problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. The solution to this problem may be characterised as the solution to a singular integral equation on the boundary. By using results of Hille and Muskhelishvili, the theory is extended to include boundaries with corners which are rarely used for numerical computation. Following Swarztrauber's derivation of an integral equation for the numerical solution of Dirichlet problem in a region of general shape, we use the Picard iteration method to obtain an iterative formula which removes singularities during numerical integration. The result is a direct method which does not involve conformal mapping. The numerical examples given demonstrate the effectiveness of this new strategy.