Abstract
In this paper, we develop a new fourth-order 9-point finite difference scheme for solving the Helmholtz equation. The central fourth-order difference scheme is used to discretize the second-order derivative, and the matched interface and boundary (MIB) method is employed to deal with the resulting boundary problem. For the discretization of the zero-order term, a weighted average method is designed by utilizing all of the 9 points, and the weight parameters are determined by minimizing the numerical dispersion. The new method is simple and efficient in suppressing the numerical dispersion. Finally, numerical examples are presented to illustrate the numerical convergence and effectiveness of the new scheme.
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