Spectral filtering methods are investigated for use in reducing the Gibbs oscillations that result when discontinuous functions are projected onto globally definedtrial function expansions. Several physical-space filters are studied in the context of a high-degree, mixed collocation method used for time integration of a nonlinear boundary value problem with a piece-wise continuous, time-dependentboundary condition. Improved accuracy is reported, both in terms of point-wiseand norm-wise solution convergence, making the filtered global collocationapproach a potential alternative to spline formulations in some applications.