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A simple trapezoidal recursive convolution (TRC) technique is used to develop a frequency-dependent FDTD method for the analysis of the Drude-critical points (D-CP) model. Numerical accuracy is investigated through the analysis of pulse propagation in a metal (aluminum) cladding waveguide. The TRC technique with a single convolution integral is found to provide the numerical results comparable to the piecewise linear RC counterparts with two convolution integrals. The D-CP model is shown to successfully yield the wide transmission spectrum that closely follows the spectrum predicted using measured permittivities, not obtainable from the Drude-Lorentz model.