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...
| Main Authors: | , , |
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| Format: | Article |
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Jabatan Matematik Fakulti Sains Universiti Teknologi Malaysia
2002
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| Online Access: | http://eprints.utm.my/3857/ |
| Summary: | 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. |
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