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

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 som...

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Main Authors: Murid, Ali Hassan Mohamed, Nasser, Mohamed M. S., Sanugi, Bahrom, Mohamad, Mohd. Nor
格式: Article
出版: Universiti Teknologi Malaysia 2004
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QA Mathematics
在線閱讀:http://eprints.utm.my/id/eprint/3852/
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spelling my.utm.38522017-10-24T07:02:16Z http://eprints.utm.my/id/eprint/3852/ The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation Murid, Ali Hassan Mohamed Nasser, Mohamed M. S. Sanugi, Bahrom Mohamad, Mohd. Nor QA Mathematics 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. Universiti Teknologi Malaysia 2004 Article PeerReviewed Murid, Ali Hassan Mohamed and Nasser, Mohamed M. S. and Sanugi, Bahrom and Mohamad, Mohd. Nor (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.
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Murid, Ali Hassan Mohamed
Nasser, Mohamed M. S.
Sanugi, Bahrom
Mohamad, Mohd. Nor
The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation
description 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.
format Article
author Murid, Ali Hassan Mohamed
Nasser, Mohamed M. S.
Sanugi, Bahrom
Mohamad, Mohd. Nor
author_facet Murid, Ali Hassan Mohamed
Nasser, Mohamed M. S.
Sanugi, Bahrom
Mohamad, Mohd. Nor
author_sort Murid, Ali Hassan Mohamed
title The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation
title_short The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation
title_full The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation
title_fullStr The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation
title_full_unstemmed The numerical solution of the non-uniquely solvable Riemann problem using a Fredholm integral equation
title_sort numerical solution of the non-uniquely solvable riemann problem using a fredholm integral equation
publisher Universiti Teknologi Malaysia
publishDate 2004
url http://eprints.utm.my/id/eprint/3852/
_version_ 1643643904435683328
score 13.250246

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