A new second-order maximum-principle preserving finite difference scheme for Allen-Cahn equations with periodic boundary conditions

DOI10.1016/j.aml.2020.106265zbMath1437.65098OpenAlexW3004640310MaRDI QIDQ2176494

Wenzhu Jiang, Defeng Xiu, Tianliang Hou

Publication date: 4 May 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106265

zbMATH Keywords

maximum principlefinite difference methoderror estimateAllen-Cahn equationenergy stability

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Second-order parabolic equations (35K10)

Related Items (15)

Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations ⋮ A second-order maximum bound principle preserving operator splitting method for the Allen-Cahn equation with applications in multi-phase systems ⋮ Up to eighth-order maximum-principle-preserving methods for the Allen-Cahn equation ⋮ Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation ⋮ An adaptive unconditional maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation ⋮ Two-grid algorithm of lumped mass finite element approximation for Allen-Cahn equations ⋮ A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation ⋮ An unconditionally stable scheme for the Allen-Cahn equation with high-order polynomial free energy ⋮ Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation ⋮ A maximum-principle preserving and unconditionally energy-stable linear second-order finite difference scheme for Allen-Cahn equations ⋮ On the preserving of the maximum principle and energy stability of high-order implicit-explicit Runge-Kutta schemes for the space-fractional Allen-Cahn equation ⋮ Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations ⋮ Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle ⋮ Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation ⋮ Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen-Cahn equations

Cites Work

• On the maximum principle preserving schemes for the generalized Allen-Cahn equation
• Numerical analysis of a stabilized Crank-Nicolson/Adams-Bashforth finite difference scheme for Allen-Cahn equations
• A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
• Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation

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