A FREQUENCY ACCURATE TEMPORAL DERIVATIVE FINITE-DIFFERENCE APPROXIMATION

A method is presented for designing temporal derivative finite differe nce approximations that achieve specified accuracy in the frequency do main. A general average value approximation with undetermined coeffici ents is fitted in the spatial frequency domain to attain the desired p roperties of the approximation. A set of constraints to insure that th e approximation convergences as the grid spacing approaches zero and s atisfies the Lax Equivalence Theorem are imposed on the fitted coeffic ients. The specification of the underlying partial differential equati on is required in order to replace the temporal frequency domain depen dence of the approximation with an explicit spatial frequency domain r elation based on the dispersion relation of the PDE. A practical desig n of the approximations is pursued using an heuristic zero placement m ethod which results in a linear matrix formulation.