A Frequency Accurate Temporal Derivative Finite Difference Approximation
Physics and Astronomy
A method is presented for designing temporal derivative finite difference approximations that achieve specified accuracy in the frequency domain. A general average value approximation with undetermined coefficients is fitted in the spatial frequency domain to attain the desired properties of the approximation. A set of constraints to insure that the approximation convergences as the grid spacing approaches zero and satisfies the Lax Equivalence Theorem are imposed on the fitted coefficients. The specification of the underlying partial differential equation is required in order to replace the temporal frequency domain dependence of the approximation with an explicit spatial frequency domain relation based on the dispersion relation of the PDE. A practical design of the approximations is pursued using an heuristic zero placement method which results in a linear matrix formulation.
Journal of Computational Acoustics
Orlin, P. A.,
Perkins, A. L.,
(1997). A Frequency Accurate Temporal Derivative Finite Difference Approximation. Journal of Computational Acoustics, 5(4), 371-382.
Available at: https://aquila.usm.edu/fac_pubs/5186