An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners
In this paper we introduce a new integral equation for computing the numerical solution of the Riemann problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. The solution to this problem may be characterised as the solution to a singular integr...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
2006
|
| Subjects: | |
| Online Access: | http://eprints.utm.my/8182/ http://dx.doi.org/10.1504/IJSPM.2006.009009 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1845471958894903296 |
|---|---|
| author | Ismail, Munira Mohd. Murid, Ali Hassan Sanugi, Bahrom |
| author_facet | Ismail, Munira Mohd. Murid, Ali Hassan Sanugi, Bahrom |
| author_sort | Ismail, Munira |
| building | UTM Library |
| collection | Institutional Repository |
| content_provider | Universiti Teknologi Malaysia |
| content_source | UTM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this paper we introduce a new integral equation for computing the numerical solution of the Riemann problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. The solution to this problem may be characterised as the solution to a singular integral equation on the boundary. By using results of Hille and Muskhelishvili, the theory is extended to include boundaries with corners which are rarely used for numerical computation. Following Swarztrauber's derivation of an integral equation for the numerical solution of Dirichlet problem in a region of general shape, we use the Picard iteration method to obtain an iterative formula which removes singularities during numerical integration. The result is a direct method which does not involve conformal mapping. The numerical examples given demonstrate the effectiveness of this new strategy |
| format | Article |
| id | my.utm.eprints-8182 |
| institution | Universiti Teknologi Malaysia |
| publishDate | 2006 |
| record_format | eprints |
| spelling | my.utm.eprints-81822017-10-12T02:01:04Z http://eprints.utm.my/8182/ An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners Ismail, Munira Mohd. Murid, Ali Hassan Sanugi, Bahrom Q Science (General) In this paper we introduce a new integral equation for computing the numerical solution of the Riemann problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. The solution to this problem may be characterised as the solution to a singular integral equation on the boundary. By using results of Hille and Muskhelishvili, the theory is extended to include boundaries with corners which are rarely used for numerical computation. Following Swarztrauber's derivation of an integral equation for the numerical solution of Dirichlet problem in a region of general shape, we use the Picard iteration method to obtain an iterative formula which removes singularities during numerical integration. The result is a direct method which does not involve conformal mapping. The numerical examples given demonstrate the effectiveness of this new strategy 2006 Article PeerReviewed Ismail, Munira and Mohd. Murid, Ali Hassan and Sanugi, Bahrom (2006) An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners. International Journal on Simulation and Process Modelling, 2 (1/2). pp. 25-32. ISSN 1740-2123 http://dx.doi.org/10.1504/IJSPM.2006.009009 10.1504/IJSPM.2006.009009 |
| spellingShingle | Q Science (General) Ismail, Munira Mohd. Murid, Ali Hassan Sanugi, Bahrom An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners |
| title | An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners |
| title_full | An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners |
| title_fullStr | An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners |
| title_full_unstemmed | An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners |
| title_short | An integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners |
| title_sort | integral equation approach for the numerical solution of the riemann problem on a simply connected region with corners |
| topic | Q Science (General) |
| url | http://eprints.utm.my/8182/ http://dx.doi.org/10.1504/IJSPM.2006.009009 |
| url_provider | http://eprints.utm.my/ |