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 - <p style="text-align: justify;">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&#39;s weight parameters. Numerical results are presented to demonstrate the efficiency and accuracy of the optimal finite difference scheme.&nbsp;</p>