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To investigate universal behavior and effects of long-range temporalcorrelations in kinetic roughening, we perform extensive simulations on theKardar-Parisi-Zhang (KPZ) equation with temporally correlated noise based onpseudospectral (PS) and one of the improved finite-difference (FD) schemes. Wefind that scaling properties are affected by long-range temporal correlationswithin the effective temporally correlated regions. Our results are consistentwith each other using these two independent numerical schemes, threecharacteristic roughness exponents (global roughness exponent $\alpha$, localroughness exponent $\alpha_{loc}$, and spectral roughness exponent$\alpha_{s}$) are approximately equal within the small temporally correlatedregime, and satisfy $\alpha_{loc} \approx \alpha<\alpha_{s}$ for the largetemporally correlated regime, and the difference between $\alpha_{s}$ and$\alpha$ increases with increasing the temporal correlation exponent $\theta$.Our results also show that PS and the improved FD schemes could effectivelysuppress numerical instabilities in the temporally correlated KPZ growthequation. Furthermore, our investigations suggest that when the effects oflong-range temporal correlation are present, the continuum and discrete growthsystems do not belong to the same universality class with the same temporalcorrelation exponent.

Improved finite-difference and pseudospectral schemes for the Kardar-Parisi-Zhang equation with long-range temporal correlations