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<p>This paper examines a new sinc-type linear numerical scheme for an epitaxial growth model. The new functional landscape is similar to that of the original model, with the added benefit that all of its derivatives are uniformly bounded. We use the Lojasiewicz–Simon inequality to establish that schema is convergent to equilibrium. We also construct a consistent numerical approach for the energy functional based on DC (difference of convex functions) programming, and study its properties taking into account these results with numerical simulations.</p>

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A sinc-type surface growth model converges to equilibrium

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Youssef Essadaoui,
  • Imad Hafidi,
  • Hamza Khalfi

摘要

This paper examines a new sinc-type linear numerical scheme for an epitaxial growth model. The new functional landscape is similar to that of the original model, with the added benefit that all of its derivatives are uniformly bounded. We use the Lojasiewicz–Simon inequality to establish that schema is convergent to equilibrium. We also construct a consistent numerical approach for the energy functional based on DC (difference of convex functions) programming, and study its properties taking into account these results with numerical simulations.