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Anomaly in Numerical Integrations of the KPZ Equation and Improved Discretization

Chi-Hang Lam·F. G. Shin
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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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Chi-Hang Lam, F. G. Shin. 1997-09-01. Anomaly in Numerical Integrations of the KPZ Equation and Improved Discretization. https://arxiv.org/abs/cond-mat/9709008

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