Title: An eight-order accurate numerical method for the solution of 2D Helmholtz equation

Authors: M. Tadi

Addresses: Department of Mechanical Engineering, University of Colorado at Denver, Campus Box 112, P.O. Box 173364, Denver, CO 80217-3364, USA

Abstract: This note is concerned with a numerical method for the solution of 2D Helmholtz equation in unit square. The method uses a finite difference approximation in one coordinate space. Similar to the method of line, the method treats the working equation as a system of ordinary differential equation in the remaining independent variable. The method uses a coordinate transformation to decouple the system of ODE. Using this procedure, it is possible to formulate numerical schemes with arbitrary orders of accuracy. Numerical results for an eight-order accurate are presented.

Keywords: Helmholtz equation; elliptic systems; high frequency; finite difference approximation; ordinary differential equations; ODEs; coordinate transformation.

DOI: 10.1504/IJCSM.2015.069458

International Journal of Computing Science and Mathematics, 2015 Vol.6 No.2, pp.122 - 128

Received: 30 Mar 2013
Accepted: 16 Dec 2013

Published online: 17 May 2015 *

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