Turkish Journal of Mathematics
DOI
10.3906/mat-1506-24
Abstract
In this paper, a modified central finite difference scheme for a three-point nonuniform grid is presented for the one-dimensional homogeneous Helmholtz equation using the Bloch wave property. The modified scheme provides highly accurate solutions at the nodes of the nonuniform grid for very small to very large range of wave numbers irrespective of how the grid is adapted throughout the domain. A variety of numerical examples are considered to validate the superiority of the modified scheme for a nonuniform grid over a standard central finite difference scheme.
Keywords
Helmholtz equation, modified central finite difference scheme, numerical dispersion, nonuniform grids, adaptive grids
First Page
806
Last Page
815
Recommended Citation
WAJID, HAFIZ ABDUL
(2016)
"Simulations of the Helmholtz equation at any wave number for adaptive grids using a modified central finite difference scheme,"
Turkish Journal of Mathematics: Vol. 40:
No.
4, Article 9.
https://doi.org/10.3906/mat-1506-24
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss4/9
