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Volume 35, Issue 3
An Optimal Sixth-Order Finite Difference Scheme for the Helmholtz Equation in One-Dimension

Xu Liu, Haina Wang & Jing Hu

Commun. Math. Res., 35 (2019), pp. 264-272.

Published online: 2019-12

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  • Abstract

In this paper, we present an optimal 3-point finite difference scheme for solving the 1D Helmholtz equation. We provide a convergence analysis to show that the scheme is sixth-order in accuracy. Based on minimizing the numerical dispersion, we propose a refined optimization rule for choosing the scheme's weight parameters. Numerical results are presented to demonstrate the efficiency and accuracy of the optimal finite difference scheme. 

  • Keywords

Helmholtz equation, finite difference method, numerical dispersion

  • AMS Subject Headings

65N06, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liuxu ping@163.com (Xu Liu)

hainawang@126.com (Haina Wang)

  • BibTex
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  • TXT
@Article{CMR-35-264, author = {Xu and Liu and liuxu ping@163.com and 6045 and chool of Applied Mathematics, Jilin University of Finance and Economics, Changchun, 130117 and Xu Liu and Haina and Wang and hainawang@126.com and 6046 and School of Applied Mathematics, Jilin University of Finance and Economics, Changchun, 130117 and Haina Wang and Jing and Hu and and 6047 and School of Applied Mathematics, Jilin University of Finance and Economics, Changchun, 130117 and Jing Hu}, title = {An Optimal Sixth-Order Finite Difference Scheme for the Helmholtz Equation in One-Dimension}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {3}, pages = {264--272}, abstract = {

In this paper, we present an optimal 3-point finite difference scheme for solving the 1D Helmholtz equation. We provide a convergence analysis to show that the scheme is sixth-order in accuracy. Based on minimizing the numerical dispersion, we propose a refined optimization rule for choosing the scheme's weight parameters. Numerical results are presented to demonstrate the efficiency and accuracy of the optimal finite difference scheme. 

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.03.07}, url = {http://global-sci.org/intro/article_detail/cmr/13531.html} }
TY - JOUR T1 - An Optimal Sixth-Order Finite Difference Scheme for the Helmholtz Equation in One-Dimension AU - Liu , Xu AU - Wang , Haina AU - Hu , Jing JO - Communications in Mathematical Research VL - 3 SP - 264 EP - 272 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.03.07 UR - https://global-sci.org/intro/article_detail/cmr/13531.html KW - Helmholtz equation, finite difference method, numerical dispersion AB -

In this paper, we present an optimal 3-point finite difference scheme for solving the 1D Helmholtz equation. We provide a convergence analysis to show that the scheme is sixth-order in accuracy. Based on minimizing the numerical dispersion, we propose a refined optimization rule for choosing the scheme's weight parameters. Numerical results are presented to demonstrate the efficiency and accuracy of the optimal finite difference scheme. 

Xu Liu, Hai-na Wang & Jing Hu. (2019). An Optimal Sixth-Order Finite Difference Scheme for the Helmholtz Equation in One-Dimension. Communications in Mathematical Research . 35 (3). 264-272. doi:10.13447/j.1674-5647.2019.03.07
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