We present a fourth-order finite difference scheme for the Helmholtz equation\nin polar coordinates. We employ the finite difference format in the interior\nof the region and derive a nine-point fourth-order scheme. Specially,\nghost points outside the region are applied to obtain the approximation for\nthe Neumann boundary condition. We obtain the matrix form of the linear\nsystem and the sparsity of the coefficient matrix is favorable for the computation\nof the Helmholtz equation. The feasibility and accuracy of the method\nare validated by two test examples which have exact solutions.
Loading....