Novel sixth-order difference scheme improves computational efficiency in solving 2D Helmholtz equation, suggesting enhanced accuracy.
This study introduces a novel approach for numerically solving the 2D Helmholtz equation. This work begins with the establishment of a sixth-order difference scheme tailored to solve the 2D Helmholtz equation under the conditions of homogeneous Dirichlet boundary and periodic boundary. Subsequently, we solve the constructed scheme using the Fast Fourier algorithm, thereby enhancing computational efficiency. Finally, to validate the efficiency and accuracy of the presented difference scheme, a series of numerical experiments were conducted.
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Xu et al. (2025) studied this question.
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