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PSpectRe, written in C++, uses Fourier-space pseudo-spectral methods to evolve interacting scalar fields in an expanding universe. The code is optimized for the analysis of parametric resonance in the post-inflationary universe and provides an alternative to finite differencing codes. PSpectRe has both second- (Velocity-Verlet) and fourth-order (Runge-Kutta) time integrators. In some circumstances PSpectRe obtains reliable results while using substantially fewer points than a finite differencing code by computing the post-resonance equation of state. PSpectRe is designed to be easily extended to other problems in early-universe cosmology, including the generation of gravitational waves during phase transitions and pre-inflationary bubble collisions.