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2014 Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number
Hafiz Abdul Wajid, Naseer Ahmed, Hifza Iqbal, Muhammad Sarmad Arshad
J. Appl. Math. 2014: 1-9 (2014). DOI: 10.1155/2014/673106

Abstract

We construct modified forward, backward, and central finite difference schemes, specifically for the Helmholtz equation, by using the Bloch wave property. All of these modified finite difference approximations provide exact solutions at the nodes of the uniform grid for the second derivative present in the Helmholtz equation and the first derivative in the radiation boundary conditions for wave propagation. The most important feature of the modified schemes is that they work for large as well as low wave numbers, without the common requirement of a very fine mesh size. The superiority of the modified finite difference schemes is illustrated with the help of numerical examples by making a comparison with standard finite difference schemes.

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Hafiz Abdul Wajid. Naseer Ahmed. Hifza Iqbal. Muhammad Sarmad Arshad. "Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/673106

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131775
MathSciNet: MR3251585
Digital Object Identifier: 10.1155/2014/673106

Rights: Copyright © 2014 Hindawi

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