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<p>The goal of this paper is to present a second-order finite difference scheme for Allen–Cahn equations with Riesz fractional derivative. The discrete maximum bound principle, the maximum-norm error estimates, and the discrete energy stability of the proposed scheme are discussed. It is shown that the proposed scheme is unconditionally energy-stable for any nonnegative stabilization parameter. Two numerical experiments are performed to verify the theoretical results.</p>

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Numerical analysis of a second-order finite difference scheme for Riesz space-fractional Allen–Cahn equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月3日

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  • Changling Xu,
  • Yang Cao,
  • Tianliang Hou

摘要

The goal of this paper is to present a second-order finite difference scheme for Allen–Cahn equations with Riesz fractional derivative. The discrete maximum bound principle, the maximum-norm error estimates, and the discrete energy stability of the proposed scheme are discussed. It is shown that the proposed scheme is unconditionally energy-stable for any nonnegative stabilization parameter. Two numerical experiments are performed to verify the theoretical results.