Solving Riemann problem using Fredholm integral equation of the second kind
To solve Riemann problem on a simply connected region, its boundary condition is transformed to a Fredholm integral equation of the second kind with continuous kernel, which is easily solved numerically. The numerical solution must satisfy an addition condition to yield a solution to the Riemann pro...
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| Materialtyp: | Artikel |
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Jabatan Matematik Fakulti Sains Universiti Teknologi Malaysia
2002
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| _version_ | 1825909456989323264 |
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| author | Murid, Ali Hassan Mohamed Razali, Mohd. R.M Nasser, Mohamed M.S. |
| author_facet | Murid, Ali Hassan Mohamed Razali, Mohd. R.M Nasser, Mohamed M.S. |
| author_sort | Murid, Ali Hassan Mohamed |
| collection | ePrints |
| description | To solve Riemann problem on a simply connected region, its boundary condition is transformed to a Fredholm integral equation of the second kind with continuous kernel, which is easily solved numerically. The numerical solution must satisfy an addition condition to yield a solution to the Riemann problem. The advantage of this approach is that we can solve Riemann problem for general simply connected region without the need to use conformal mapping. Some numerical implementations are presented. |
| first_indexed | 2024-03-05T18:02:26Z |
| format | Article |
| id | utm.eprints-3857 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T18:02:26Z |
| publishDate | 2002 |
| publisher | Jabatan Matematik Fakulti Sains Universiti Teknologi Malaysia |
| record_format | dspace |
| spelling | utm.eprints-38572017-10-24T07:05:01Z http://eprints.utm.my/3857/ Solving Riemann problem using Fredholm integral equation of the second kind Murid, Ali Hassan Mohamed Razali, Mohd. R.M Nasser, Mohamed M.S. QA Mathematics To solve Riemann problem on a simply connected region, its boundary condition is transformed to a Fredholm integral equation of the second kind with continuous kernel, which is easily solved numerically. The numerical solution must satisfy an addition condition to yield a solution to the Riemann problem. The advantage of this approach is that we can solve Riemann problem for general simply connected region without the need to use conformal mapping. Some numerical implementations are presented. Jabatan Matematik Fakulti Sains Universiti Teknologi Malaysia 2002 Article PeerReviewed Murid, Ali Hassan Mohamed and Razali, Mohd. R.M and Nasser, Mohamed M.S. (2002) Solving Riemann problem using Fredholm integral equation of the second kind. Prosiding Simposium Kebangsaan Sains Matematik Ke-10 Jabatan Matematik Fakulti Sains Universiti Teknologi Malaysia dan Persatuan Sains Matematik Malaysia . pp. 171-178. |
| spellingShingle | QA Mathematics Murid, Ali Hassan Mohamed Razali, Mohd. R.M Nasser, Mohamed M.S. Solving Riemann problem using Fredholm integral equation of the second kind |
| title | Solving Riemann problem using Fredholm integral equation of the second kind |
| title_full | Solving Riemann problem using Fredholm integral equation of the second kind |
| title_fullStr | Solving Riemann problem using Fredholm integral equation of the second kind |
| title_full_unstemmed | Solving Riemann problem using Fredholm integral equation of the second kind |
| title_short | Solving Riemann problem using Fredholm integral equation of the second kind |
| title_sort | solving riemann problem using fredholm integral equation of the second kind |
| topic | QA Mathematics |
| work_keys_str_mv | AT muridalihassanmohamed solvingriemannproblemusingfredholmintegralequationofthesecondkind AT razalimohdrm solvingriemannproblemusingfredholmintegralequationofthesecondkind AT nassermohamedms solvingriemannproblemusingfredholmintegralequationofthesecondkind |