On a technique for high accuracy of discretizing spatial derivatives

An analysis is given for numerical dispersion associated with a linear, one-dimensional dispersion equation in cases where the space derivative is discretized by a higher-order numerical scheme. A very significant elimination of phase speed error is demonstrated, by comparison with alternative finite difference schemes. Although essentially derived from the finite Fourier transform, the method bypasses calculations using the transform algorithm required by the spectral or pseudospectral technique.