Sutmann, G. (2007) Compact Finite Difference Schemes of Sixth-Order for the Helmholtz Equation. Journal of Computational and Applied Mathematics, 203, 15-31.
https://doi.org/10.1016/j.cam.2006.03.008

has been cited by the following article:

• TITLE: High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates

  AUTHORS: Na Zhu, Meiling Zhao

  KEYWORDS: High-Order, Helmholtz Equation, Polar Coordinates

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.9 No.3, August 30, 2019

  ABSTRACT: We present a fourth-order finite difference scheme for the Helmholtz equation in polar coordinates. We employ the finite difference format in the interior of the region and derive a nine-point fourth-order scheme. Specially, ghost points outside the region are applied to obtain the approximation for the Neumann boundary condition. We obtain the matrix form of the linear system and the sparsity of the coefficient matrix is favorable for the computation of the Helmholtz equation. The feasibility and accuracy of the method are validated by two test examples which have exact solutions.