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.
Biazar, J., Asayesh, R. (2020). An efficient high-order compact finite difference method for the Helmholtz equation. Computational Methods for Differential Equations, 8(3), 553-563. doi: 10.22034/cmde.2020.27993.1382
MLA
Jafar Biazar; Roxana Asayesh. "An efficient high-order compact finite difference method for the Helmholtz equation". Computational Methods for Differential Equations, 8, 3, 2020, 553-563. doi: 10.22034/cmde.2020.27993.1382
HARVARD
Biazar, J., Asayesh, R. (2020). 'An efficient high-order compact finite difference method for the Helmholtz equation', Computational Methods for Differential Equations, 8(3), pp. 553-563. doi: 10.22034/cmde.2020.27993.1382
VANCOUVER
Biazar, J., Asayesh, R. An efficient high-order compact finite difference method for the Helmholtz equation. Computational Methods for Differential Equations, 2020; 8(3): 553-563. doi: 10.22034/cmde.2020.27993.1382
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