Anomaly in Numerical Integrations of the KPZ Equation and Improved Discretization
Chi-Hang Lam, F. G. Shin
Abstract
We demonstrate and explain that conventional finite difference schemes for direct numerical integration do not approximate the continuum Kardar-Parisi-Zhang (KPZ) equation due to microscopic roughness. The effective diffusion coefficient is found to be inconsistent with the nominal one. We propose a novel discretization in 1+1 dimensions which does not suffer from this deficiency and elucidates the reliability and limitations of direct integration approaches.
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