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The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation

Murid, Ali H. M. and Nasser, Mohamed M. S. and Sanugi, Bahrom and Mohamad, Mohd N. (2004) The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation. Proceedings of the 2nd Annual Fundamental Science Seminar 2004, AFSS 2004 . pp. 289-295.

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Abstract

This paper is devoted to the computational aspect of the Riemann problem with non-unique solution in a simply connected region with smooth boundary. The boundary condition of the Riemann problem is transformed to a Fredholm integral equation of the second kind with continuous kernel. By imposing some side conditions, the integral equation can be solved using Nystrom method. The equivalence of the integral equation and the Riemann problem will be established for any smmoth Jordan curve. Typical examples illustrate that numerical results of high accuracy can be obtained provided that the boundaries are sufficiently smooth.

Item Type:Article
Uncontrolled Keywords:Riemann problem, Fredholm integral equation, eigenvalue, index of functions.
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:3852
Deposited By: Assoc. Prof. Dr. Ali Hassan Mohamed Murid
Deposited On:27 Jun 2007 08:33
Last Modified:29 Jun 2007 02:06

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