University of Tabriz Computational Methods for Differential Equations 2345-3982 8 3 2020 08 01 An efficient high-order compact finite difference method for the Helmholtz equation 553 563 9910 10.22034/cmde.2020.27993.1382 EN Jafar Biazar Department of Applied Mathematics, University of Guilan, P. O. Box. 41635-19141, P. C. 41938336997, Rasht, Iran. Roxana Asayesh Department of Applied Mathematics, University of Guilan, P. O. Box. 41635-19141, P. C. 41938336997, Rasht, Iran. Journal Article 2018 06 19 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. https://cmde.tabrizu.ac.ir/article_9910_3b6fe6a49e477ad98e3912767be69d04.pdf