Up to eighth-order maximum-principle-preserving methods for the Allen-Cahn equation
DOI10.1007/s11075-022-01329-4OpenAlexW4283734935WikidataQ114224269 ScholiaQ114224269MaRDI QIDQ2679814
Jingwei Sun, Songhe Song, Hong Zhang, Xu Qian
Publication date: 26 January 2023
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-022-01329-4
Maximum principles in context of PDEs (35B50) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Partial differential equations of mathematical physics and other areas of application (35Q99) Integro-partial differential equations (35R09)
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Cites Work
- 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
- The explicit-implicit-null method: removing the numerical instability of PDEs
- A linear iteration algorithm for a second-order energy stable scheme for a thin film model without slope selection
- An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
- Construction of two-step Runge--Kutta methods with large regions of absolute stability
- 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
- A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation
- Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations
- 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
- 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
- Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic 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
- A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
- Third-order conservative sign-preserving and steady-state-preserving time integrations and applications in stiff multispecies and multireaction detonations
- Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
- 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
- Strong Stability-Preserving High-Order Time Discretization Methods
- Strong Stability Preserving Two-step Runge–Kutta Methods
- A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities
- Two-Step Runge–Kutta Methods
- Numerical Analysis of a Continuum Model of Phase Transition
- Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
- Phase transitions and generalized motion by mean curvature
- The Global Dynamics of Discrete Semilinear Parabolic Equations
- Total variation diminishing Runge-Kutta schemes
- Strong Stability Preserving Integrating Factor Runge--Kutta Methods
- Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
- A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
- 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
- Arbitrarily High-Order Exponential Cut-Off Methods for Preserving Maximum Principle of Parabolic Equations
- Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
- Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations
- Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
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