Stability and robustness of time-discretization schemes for the Allen-Cahn equation via bifurcation and perturbation analysis

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Cites Work

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On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework
An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Elements of applied bifurcation theory.
Applications of semi-implicit Fourier-spectral method to phase field equations
Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
Multi-phase-field modeling using a conservative Allen-Cahn equation for multiphase flow
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
Geometrical image segmentation by the Allen-Cahn equation
On the stability and accuracy of partially and fully implicit schemes for phase field modeling
An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs
Time-fractional Allen-Cahn equations: analysis and numerical methods
Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
On the preserving of the maximum principle and energy stability of high-order implicit-explicit Runge-Kutta schemes for the space-fractional Allen-Cahn equation
Diagonally implicit Runge-Kutta methods for stiff ODEs
A homotopy method with adaptive basis selection for computing multiple solutions of differential equations
Image segmentation based on modified fractional Allen-Cahn equation
An adaptive homotopy method for computing bifurcations of nonlinear parametric systems
Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models
Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
On linear schemes for a Cahn-Hilliard diffuse interface model
Topics in stability and bifurcation theory
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations
Time discretizations of anisotropic Allen-Cahn equations
Spectral approximation of pattern-forming nonlinear evolution equations with double-well potentials of quadratic growth
Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
Efficient numerical scheme for solving the Allen‐Cahn equation
Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
Convergence analysis of the semi-implicit euler method for abstract evolution equations
High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics
Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models
Lack of robustness and accuracy of many numerical schemes for phase-field simulations

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