IJPAM: Volume 31, No. 3 (2006)


Munira Ismail$^1$, Bahrom Sanugi$^2$, Ali Hassan Mohd Murid$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Science
University of Technology of Malaysia
81310 UTM Skudai, Johor Darul Ta'zim, MALAYSIA
$^1$e-mail: mi@mel.fs.utm.my
$^2$e-mail: bs@mel.fs.utm.my
$^3$e-mail: ahmm@mel.fs.utm.my

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