Uzunca, MuratKarasozen, Buelent2025-03-232025-03-2320230096-30031873-5649https://doi.org/10.1016/j.amc.2023.127984https://hdl.handle.net/11486/6714It is well known that the Allen-Cahn equation satisfies a nonlinear stability property, i.e., the free-energy functional decreases in time. Linearly implicit integrators have been de-veloped for energy-preserving methods for conservative systems with polynomial Hamil-tonians, which are based on the concept of polarization. In this paper, we construct lin-early implicit methods for gradient flows preserving the energy dissipation by polarizing the free-energy functional. Two-step linearly implicit methods are derived for the Allen -Cahn equation inheriting energy dissipation law. Numerical experiments for one-, two-, and three-dimensional Allen-Cahn equations demonstrate the energy dissipation and the accuracy of the linearly implicit methods.(c) 2023 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessAllen -Cahn equationGradient systemsEnergy dissipationLinearly implicit methodsArticle45010.1016/j.amc.2023.1279842-s2.0-85150901804Q1WOS:000965266700001Q1