IJPAM: Volume 31, No. 3 (2006)
BOUNDARY INTEGRAL EQUATION WITH CORNERS




Faculty of Science
University of Technology of Malaysia
81310 UTM Skudai, Johor Darul Ta'zim, MALAYSIA



Abstract.This paper offers an effective
technique for seeking numerical solution of the interior Riemann
problem on a simply connected region with a finite number of
corners by Picard iteration method. Previously we have obtained
an integral equation associated with the problem and constructed
an iterative formula that facilitated numerical integrations.
Numerical examples presented in this paper reveal that solutions
obtained by applying Gaussian quadrature are excellent, however it
can only provide solution values at off-corner points. In this
paper, we constructed a new iterative technique that interpolate
solution at each corner point using the values we obtained at
off-corner points. By this technique the problem of finding
solution at the corners is resolve since we are able to maintain
excellent accuracy of solutions everywhere on the boundary
including the corners. Proofs of the solvability and uniqueness of
the integral equation and its equivalence to the problem are also
included.
Received: August 11, 2006
AMS Subject Classification: 30E25, 45B05, 30C30
Key Words and Phrases: interior Riemann problem, Fredholm integral equation, Picard iteration method
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 3