Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number
Joint Authors
Arshad, Muhammad Sarmad
Iqbal, Hifza
Ahmed, Naseer
Wajid, Hafiz Abdul
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-11
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Wajid, Hafiz Abdul& Ahmed, Naseer& Iqbal, Hifza& Arshad, Muhammad Sarmad. 2014. Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-489364
Modern Language Association (MLA)
Wajid, Hafiz Abdul…[et al.]. Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number. Journal of Applied Mathematics No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-489364
American Medical Association (AMA)
Wajid, Hafiz Abdul& Ahmed, Naseer& Iqbal, Hifza& Arshad, Muhammad Sarmad. Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-489364
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-489364