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A High-Order Discrete Energy Decay and Maximum-Principle Preserving Scheme for Time Fractional Allen–Cahn Equation
The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional...
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The Exponential SAV Approach for the Time-Fractional Allen–Cahn and Cahn–Hilliard Phase-Field Models
In this paper, we take a consideration of a class of time-fractional phase-field models including the Allen–Cahn and Cahn–Hilliard equations. Based...
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Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen–Cahn Equation
The convective Allen–Cahn (CAC) equation has been widely used for simulating multiphase flows of incompressible fluids, which contains an extra...
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Second-Order Error Analysis for Fractal Mobile/Immobile Allen–Cahn Equation on Graded Meshes
The fractal mobile/immobile model bridges between Fickian fluxes at early times and non-Gaussian behavior at late times. In this work, an averaged L1...
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Maximum bound principle preserving linear schemes for nonlocal Allen–Cahn equation based on the stabilized exponential-SAV approach
The nonlocal Allen–Cahn equation with nonlocal diffusion operator is important for simulating a series of physical and biological phenomena involving...
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Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen–Cahn equations
In this paper, we construct a new linear second-order finite difference scheme with two parameters for space-fractional Allen–Cahn equations. We...
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Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations
In this paper, a numerical method to solve the multi-dimensional spatial fractional Allen–Cahn equations has been investigated. After...
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Numerical investigation into the dependence of the Allen–Cahn equation on the free energy
Phase-field modeling is strongly influenced by the shape of a free energy functional. In the theory of thermodynamics, it is a logarithmic type...
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Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility
We consider the sharp interface limit of a Navier–Stokes/Allen Cahn equation in a bounded smooth domain in two space dimensions, in the case of...
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Time-Fractional Allen–Cahn Equations: Analysis and Numerical Methods
In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first order time derivative is replaced by a Caputo...
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Operator splitting scheme based on barycentric Lagrange interpolation collocation method for the Allen-Cahn equation
In this paper, we consider the operator splitting scheme based on barycentric Lagrange interpolation collocation method for the two-dimensional...
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On Diagonal Dominance of FEM Stiffness Matrix of Fractional Laplacian and Maximum Principle Preserving Schemes for the Fractional Allen–Cahn Equation
In this paper, we study diagonal dominance of the stiffness matrix resulted from the piecewise linear finite element discretisation of the integral...
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Stabilized Exponential-SAV Schemes Preserving Energy Dissipation Law and Maximum Bound Principle for The Allen–Cahn Type Equations
It is well-known that the Allen–Cahn equation not only satisfies the energy dissipation law but also possesses the maximum bound principle (MBP) in...
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A Dimensional Splitting Exponential Time Differencing Scheme for Multidimensional Fractional Allen-Cahn Equations
This paper is concerned with numerical methods for solving the multidimensional Allen-Cahn equations with spatial fractional Riesz derivatives. A...
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Explicit Third-Order Unconditionally Structure-Preserving Schemes for Conservative Allen–Cahn Equations
Compared with the well-known classical Allen–Cahn equation, the modified Allen–Cahn equation, which is equipped with a nonlocal Lagrange multiplier...
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Simple maximum principle preserving time-step** methods for time-fractional Allen-Cahn equation
Two fast L1 time-step** methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional...
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Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen–Cahn Equation with Nonlocal Constraint
In comparison with the Cahn–Hilliard equation, the classic Allen-Cahn equation satisfies the maximum bound principle (MBP) but fails to conserve the...
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A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions
We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate...
