An efficient high-order compact finite difference method for the Helmholtz equation

Document Type : Research Paper


Department of Applied Mathematics, University of Guilan, P. O. Box. 41635-19141, P. C. 41938336997, Rasht, Iran.


This paper is devoted to applying the sixth-order compact finite difference approach to the Helmholtz equation. Instead of using matrix inversion, a discrete sinusoidal transform is used as a quick solver to solve the discretized system resulted from the compact finite difference method. Through this way, the computational costs of the method with large numbers of nodes are greatly reduced. The efficiency and accuracy of the scheme are investigated by solving some illustrative examples, having the exact solutions.


Volume 8, Issue 3
August 2020
Pages 553-563
  • Receive Date: 19 June 2018
  • Revise Date: 10 April 2019
  • Accept Date: 15 April 2019
  • First Publish Date: 01 August 2020