Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation
DOI10.1016/j.camwa.2022.10.023zbMath1504.65172OpenAlexW4308749536MaRDI QIDQ2107202
Publication date: 1 December 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2022.10.023
high performanceerror estimationsdiscrete energy-dissipation lawsenergy-dissipation-preserving ADI methodsnonlinear Allen-Cahn equation
Reaction-diffusion equations (35K57) 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)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation
- Optimal point-wise error estimate of a compact difference scheme for the coupled Gross-Pitaevskii equations in one dimension
- Numerical simulation of the three dimensional Allen-Cahn equation by the high-order compact ADI method
- Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
- Generation, propagation, and annihilation of metastable patterns
- Travelling wave solutions of the Cahn-Allen equation by using first integral method
- Infinite-dimensional dynamical systems in mechanics and physics
- Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
- Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
- A new fourth-order numerical algorithm for a class of nonlinear wave equations
- An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations
- Geometrical image segmentation by the Allen-Cahn equation
- A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations
- The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction-diffusion equations with variable coefficients
- Linear energy stable and maximum principle preserving semi-implicit scheme for Allen-Cahn equation with double well potential
- The discrete maximum principle and energy stability of a new second-order difference scheme for Allen-Cahn equations
- Fast, provably unconditionally energy stable, and second-order accurate algorithms for the anisotropic Cahn-Hilliard model
- 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
- Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation
- An unconditional stable compact fourth-order finite difference scheme for three dimensional Allen-Cahn equation
- A SCR-based error estimation and adaptive finite element method for the Allen-Cahn equation
- A maximum-principle preserving and unconditionally energy-stable linear second-order finite difference scheme for Allen-Cahn equations
- Convergence analysis for the invariant energy quadratization (IEQ) schemes for solving the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential
- A novel linear second order unconditionally energy stable scheme for a hydrodynamic \(\mathbf{Q} \)-tensor model of liquid crystals
- The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations
- The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
- A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
- The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations
- The multistep finite difference fractional steps method for a class of viscous wave equations
- Analysis of some finite difference schemes for two-dimensional Ginzburg-Landau equation
- A bifurcation problem for a nonlinear partial differential equation of parabolic type†
- The Global Dynamics of Discrete Semilinear Parabolic Equations
- An efficient high-order algorithm for solving systems of reaction-diffusion equations
- Phase-Field Models for Multi-Component Fluid Flows
- An economical difference scheme for heat transport equation at the microscale
- Metastable patterns in solutions of ut = ϵ2uxx − f(u)
- Numerical analysis of a conservative linear compact difference scheme for the coupled Schrödinger–Boussinesq equations
- Maximum norm error analysis of an unconditionally stable semi‐implicit scheme for multi‐dimensional Allen–Cahn equations
- Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
- Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
- Discrete maximum-norm stability of a linearized second-order finite difference scheme for Allen–Cahn equation
- Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights
This page was built for publication: Efficiently energy-dissipation-preserving ADI methods for solving two-dimensional nonlinear Allen-Cahn equation