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DOI: 10.23952/jnfa.2025.8
Received December 10, 2024; Accepted March 3, 2025; Published March 25, 2025
Abstract. This paper aims to present a linearized second-order finite difference scheme for Allen-Cahn equations with Riesz fractional derivative and logarithmic free energy. First, the discrete maximum bound principle of the proposed scheme is discussed. Second, the discrete energy stability with classical energy is derived. Subsequently, a new discrete energy is defined and proven to be unconditionally decreasing. Finally, a numerical experiment is carried out to verify the theoretical results.
How to Cite this Article:
X. Wu, T. Hou, A linearized second-order finite difference scheme for Riesz space-fractional Allen-Cahn equations with logarithmic free energy, J. Nonlinear Funct. Anal. 2025 (2025) 8.