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A simple trapezoidal recursive convolution technique is utilized to develop a frequency-dependent locally one-dimensional finite-difference time-domain (FDTD) method for the three-dimensional analysis of dispersive media. A gap plasmonic waveguide is analyzed and the numerical results are compared with those of the traditional explicit FDTD. A time step ten times as large as that determined from the stability criterion can be allowed to reduce computational time by 40%, offering acceptable numerical results. A plasmonic grating is analyzed as an application.