Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/673106 |
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| _version_ | 1832555917179092992 |
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| author | Hafiz Abdul Wajid Naseer Ahmed Hifza Iqbal Muhammad Sarmad Arshad |
| author_facet | Hafiz Abdul Wajid Naseer Ahmed Hifza Iqbal Muhammad Sarmad Arshad |
| author_sort | Hafiz Abdul Wajid |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4245b9dac7704f8fb05fc534e146f7fb |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4245b9dac7704f8fb05fc534e146f7fb2025-02-03T05:46:52ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/673106673106Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave NumberHafiz Abdul Wajid0Naseer Ahmed1Hifza Iqbal2Muhammad Sarmad Arshad3Department of Mathematics, COMSATS Institute of Information Technology, Lahore 54000, PakistanDepartment of Mechanical Engineering, Faculty of Engineering, CECOS University of IT and Emerging Sciences, Peshawar 25000, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore 54000, PakistanDepartment of Mathematics, University College of Engineering, Sciences and Technology, Lahore Leads University, Lahore 54000, PakistanWe 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.http://dx.doi.org/10.1155/2014/673106 |
| spellingShingle | 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 Journal of Applied Mathematics |
| title | Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number |
| title_full | Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number |
| title_fullStr | Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number |
| title_full_unstemmed | Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number |
| title_short | Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number |
| title_sort | modified finite difference schemes on uniform grids for simulations of the helmholtz equation at any wave number |
| url | http://dx.doi.org/10.1155/2014/673106 |
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