Anomaly in Numerical Integrations of the KPZ Equation and Improved Discretization

1997/09/01 by Chi-Hang Lam, C.M. Lam, Lam, Chi-Hang +2
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #FOS: Physical sciences #Fractional Differential Equations Solutions #Numerical methods for differential equations #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/9709008

14 pages, 3 figures, RevTex

arxiv created 1997/09/01 · openalex publication_date 1997/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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