Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation

Maximum principles in context of PDEs (35B50) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Cites Work

Unnamed Item
An \(H^2\) convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn-Hilliard equation
On the maximum principle preserving schemes for the generalized Allen-Cahn equation
Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
Exponential time differencing for stiff systems
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
On large time-stepping methods for the Cahn-Hilliard equation
Modelling phase transitions in alloys
Contractivity of Runge-Kutta methods
Applications of semi-implicit Fourier-spectral method to phase field equations
Removing the stiffness from interfacial flows with surface tension
Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms
Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
The scalar auxiliary variable (SAV) approach for gradient flows
Geometrical image segmentation by the Allen-Cahn equation
On the stability and accuracy of partially and fully implicit schemes for phase field modeling
Analysis of fully discrete approximations for dissipative systems and application to time-dependent nonlocal diffusion problems
Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach
Linearly stabilized schemes for the time integration of stiff nonlinear PDEs
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
Time-accurate and highly-stable explicit operators for stiff differential equations
Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations
A note on the stability of time-accurate and highly-stable explicit operators for stiff differential equations
Energy-decreasing exponential time differencing Runge-Kutta methods for phase-field models
Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations
Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen-Cahn type equations
A new second-order maximum-principle preserving finite difference scheme for Allen-Cahn equations with periodic boundary conditions
A fast and efficient numerical algorithm for fractional Allen-Cahn with precise nonlocal mass conservation
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
An efficient explicit full-discrete scheme for strong approximation of stochastic Allen-Cahn equation
Efficient numerical scheme for a dendritic solidification phase field model with melt convection
Third-order conservative sign-preserving and steady-state-preserving time integrations and applications in stiff multispecies and multireaction detonations
A roadmap for discretely energy-stable schemes for dissipative systems based on a generalized auxiliary variable with guaranteed positivity
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
A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation
Convergence analysis for the invariant energy quadratization (IEQ) schemes for solving the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential
Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
Fast explicit integration factor methods for semilinear parabolic equations
Fast high-order compact exponential time differencing Runge-Kutta methods for second-order semilinear parabolic equations
Stability and Error Estimates of Local Discontinuous Galerkin Methods with Implicit-Explicit Time-Marching for Advection-Diffusion Problems
Solving Ordinary Differential Equations I
Runge-Kutta Methods with Minimum Error Bounds
Phase transitions and generalized motion by mean curvature
Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
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
Efficient numerical methods for phase-field equations
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows
The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing
Global Constraints Preserving Scalar Auxiliary Variable Schemes for Gradient Flows
Arbitrarily High-Order Exponential Cut-Off Methods for Preserving Maximum Principle of Parabolic Equations
Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation
Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator
Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions
Temporal high-order, unconditionally maximum-principle-preserving integrating factor multi-step methods for Allen-Cahn-type parabolic equations
High-order, unconditionally maximum-principle preserving finite element method for the Allen-Cahn equation

This page was built for publication: Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation