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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Universiti Teknologi Malaysia
2004
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| Online Access: | http://eprints.utm.my/3852/ |
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| 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 |
| building | UTM Library |
| collection | Institutional Repository |
| content_provider | Universiti Teknologi Malaysia |
| content_source | UTM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| 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 |
| id | my.utm.eprints-3852 |
| institution | Universiti Teknologi Malaysia |
| publishDate | 2004 |
| publisher | Universiti Teknologi Malaysia |
| record_format | eprints |
| spelling | my.utm.eprints-38522017-10-24T07:02:16Z http://eprints.utm.my/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. |
| 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 |
| title | 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_short | 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 |
| topic | QA Mathematics |
| url | http://eprints.utm.my/3852/ |
| url_provider | http://eprints.utm.my/ |