A linear second-order maximum bound principle preserving finite difference scheme for the generalized Allen-Cahn equation

DOI10.1016/J.AML.2024.109250zbMATH Open1547.6511MaRDI QIDQ6592488

Zirui Du, Tianliang Hou

Publication date: 26 August 2024

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

zbMATH Keywords

finite difference methoderror estimategeneralized Allen-Cahn equationmaximum bound principle

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Maximum principles in context of PDEs (35B50) 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)

Cites Work

• On the maximum principle preserving schemes for the generalized Allen-Cahn equation
• Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
• Geometrical image segmentation by the Allen-Cahn equation
• A new second-order maximum-principle preserving finite difference scheme for Allen-Cahn equations with periodic boundary conditions
• Numerical analysis of a stabilized Crank-Nicolson/Adams-Bashforth finite difference scheme for Allen-Cahn equations
• A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities
• Phase-Field Models for Multi-Component Fluid Flows
• Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
• A linear doubly stabilized Crank-Nicolson scheme for the Allen-Cahn equation with a general mobility

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