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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

DOI: 10.13447/j.1674-5647.2019.03.07

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
  • RIS
  • TXT
@Article{CMR-35-264, author = {Liu , XuWang , Haina and Hu , Jing}, 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. 

Liu , XuWang , Haina and Hu , Jing. (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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