The conventional FD (finite-difference) operators on time and space derivatives are designed in the space and time domains independently. In this paper, we propose an entirely new approach in that we first represent the derivative operators in terms of a series. This is followed by substituting a plane wave trial solution - the resulting equations are made to satisfy grid dispersion criteria and then solved for the coefficients in the series representation of derivatives. Thus unlike a conventional FD scheme, coefficients are determined a posteriori in our approach. Dispersion analysis and modeling results under the same discretization demonstrate that the new method requires the same computation time and resources as that of a conventional FD but attains a greater accuracy.
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