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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Bibliographic Details
Main Authors: Murid, Ali Hassan Mohamed, Razali, Mohd. R.M, Nasser, Mohamed M.S.
Format: Article
Published: Jabatan Matematik Fakulti Sains Universiti Teknologi Malaysia 2002
Subjects:
Online Access:http://eprints.utm.my/3857/
Description
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.