Abstract
A sixth order quasi-compact finite difference (SQC) scheme for the Helmholtz equation with variable wave numbers in two and three dimensional rectangular domains has been developed and analyzed. The finite difference coefficients for the solution and the weights for the source term have explicit expressions without involving derivatives of the source term. The proof of the sixth order convergence of the new method is also presented. Numerical experiments presented in this paper confirmed the order of convergence of the new method.
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