@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} }