Temporal high-order, unconditionally maximum-principle-preserving integrating factor multi-step methods for Allen-Cahn-type parabolic equations

DOI10.1016/j.apnum.2022.12.020OpenAlexW4313560907MaRDI QIDQ6101775

Hong Zhang, Xu Qian, Songhe Song, JingYe Yan

Publication date: 20 June 2023

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2022.12.020

zbMATH Keywords

mass conservationmaximum-principle-preservingAllen-Cahn-type equationparametric integrating factor multi-step scheme

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Parabolic equations and parabolic systems (35Kxx)

Related Items (3)

Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions ⋮ A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation ⋮ Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation

Cites Work

• Unnamed Item
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• On the maximum principle preserving schemes for the generalized Allen-Cahn equation
• Convergence of a mass conserving Allen-Cahn equation whose Lagrange multiplier is nonlocal and local
• Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
• On high order strong stability preserving Runge-Kutta and multi step time discretizations
• Generalized integrating factor methods for stiff PDEs
• Positivity of exponential Runge-Kutta methods
• Circle contractive linear multistep methods
• Contractivity preserving explicit linear multistep methods
• Contractivity of Runge-Kutta methods
• A conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier
• Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms
• A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
• On the stability and accuracy of partially and fully implicit schemes for phase field modeling
• The discrete maximum principle and energy stability of a new second-order difference scheme for Allen-Cahn equations
• Unconditionally maximum bound principle preserving linear schemes for the conservative Allen-Cahn equation with nonlocal constraint
• Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations
• Arbitrarily high-order maximum bound preserving schemes with cut-off postprocessing for Allen-Cahn equations
• Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations
• The high-order maximum-principle-preserving integrating factor Runge-Kutta methods for nonlocal Allen-Cahn equation
• Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations
• 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 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
• Fast explicit operator splitting method and time-step adaptivity for fractional non-local Allen-Cahn model
• Strong stability preserving integrating factor two-step Runge-Kutta methods
• A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation
• Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
• High-order linear multistep methods with general monotonicity and boundedness properties
• Fast explicit integration factor methods for semilinear parabolic equations
• Strong Stability-Preserving High-Order Time Discretization Methods
• Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations
• A modified phase field approximation for mean curvature flow with conservation of the volume
• An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
• The phase field method for geometric moving interfaces and their numerical approximations
• Nonlocal reaction—diffusion equations and nucleation
• Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials
• Fully Discrete Second-Order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluid Flows with Variable Densities
• High-Order Bound-Preserving Discontinuous Galerkin Methods for Stiff Multispecies Detonation
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS
• TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER
• Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
• Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle
• Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows
• Arbitrarily High-Order Exponential Cut-Off Methods for Preserving Maximum Principle of Parabolic Equations
• Effective Maximum Principles for Spectral Methods

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