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Maxwell's curl equations in the time domain are cast into a conservation form and discretized using a finite-volume procedure. The Lax-Wendroff explicit scheme is then used to solve the discretized Maxwell's equations, resulting in second-order accuracy with respect to both time and space. This time-domain scheme does not require an interlaced mesh for electric and magnetic fields. Radiation pattern and input impedance of some typical parallel-plate waveguides and mutual coupling for arrays of parallel-plate waveguides are computed and, whenever possible, compared with closed form exact or approximate solutions. Radiation patterns for a two-dimensional horn and a rectangular waveguide are presented.