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

Zhu, Na and Zhao, Meiling (2019) High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates. American Journal of Computational Mathematics, 09 (03). pp. 174-186. ISSN 2161-1203

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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.

Item Type: Article
Subjects: Digital Open Archives > Mathematical Science
Depositing User: Unnamed user with email support@digiopenarchives.com
Date Deposited: 16 Jun 2023 06:35
Last Modified: 18 Oct 2024 04:26
URI: http://geographical.openuniversityarchive.com/id/eprint/1460

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