Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows

Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations

(2022) Jiang Yang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Generalized SAV approaches for gradient systems

(2021) Qing Cheng et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Unconditionally Maximum Bound Principle Preserving Linear Schemes for the Conservative Allen–Cahn Equation with Nonlocal Constraint

(2021) Jingwei Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations

(2021) Lili Ju et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Error Estimate of a Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Epitaxial Thin Film Equation

(2021) global sci   Advances in Applied Mathematics and Mechanics

Convergence Analysis for the Invariant Energy Quadratization (IEQ) Schemes for Solving the Cahn–Hilliard and Allen–Cahn Equations with General Nonlinear Potential

(2020) Xiaofeng Yang et al.   JOURNAL OF SCIENTIFIC COMPUTING

A new Lagrange multiplier approach for gradient flows

(2020) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation

(2020) Chaolong Jiang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Mass- and energy-preserving exponential Runge–Kutta methods for the nonlinear Schrödinger equation

(2020) Jin Cui et al.   APPLIED MATHEMATICS LETTERS

Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation

(2020) Hong Zhang et al.   APPLIED NUMERICAL MATHEMATICS

Efficient and linear schemes for anisotropic Cahn–Hilliard model using the Stabilized-Invariant Energy Quadratization (S-IEQ) approach

(2019) Zhen Xu et al.   COMPUTER PHYSICS COMMUNICATIONS

A Third Order Exponential Time Differencing Numerical Scheme for No-Slope-Selection Epitaxial Thin Film Model with Energy Stability

(2019) Kelong Cheng et al.   JOURNAL OF SCIENTIFIC COMPUTING

Energy-stable Runge–Kutta schemes for gradient flow models using the energy quadratization approach

(2019) Yuezheng Gong et al.   APPLIED MATHEMATICS LETTERS

A variant of scalar auxiliary variable approaches for gradient flows

(2019) Dianming Hou et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

(2018) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Numerical Analysis of Fully Discretized Crank–Nicolson Scheme for Fractional-in-Space Allen–Cahn Equations

(2017) Tianliang Hou et al.   JOURNAL OF SCIENTIFIC COMPUTING

Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection

(2017) Lili Ju et al.   MATHEMATICS OF COMPUTATION

On the maximum principle preserving schemes for the generalized Allen–Cahn equation

(2016) Jie Shen et al.   Communications in Mathematical Sciences

Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle

(2016) Tao Tang et al.   JOURNAL OF COMPUTATIONAL MATHEMATICS

Traveling wave solutions of Allen–Cahn equation with a fractional Laplacian

(2015) Changfeng Gui et al.   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

Fast High-Order Compact Exponential Time Differencing Runge–Kutta Methods for Second-Order Semilinear Parabolic Equations

(2015) Liyong Zhu et al.   JOURNAL OF SCIENTIFIC COMPUTING

Fast Explicit Integration Factor Methods for Semilinear Parabolic Equations

(2014) Lili Ju et al.   JOURNAL OF SCIENTIFIC COMPUTING

Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection

(2014) Zhonghua Qiao et al.   MATHEMATICS OF COMPUTATION

A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation

(2014) Zhen Guan et al.   NUMERISCHE MATHEMATIK

Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models

(2013) Xinlong Feng et al.   East Asian Journal on Applied Mathematics

Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy

(2012) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

The Cahn-Hilliard Equation with Logarithmic Potentials

(2011) Laurence Cherfils et al.   Milan Journal of Mathematics

An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models

(2011) Zhonghua Qiao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

(2010) Jie Shen et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Exponential integrators

(2010) Marlis Hochbruck et al.   ACTA NUMERICA

An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation

(2009) S. M. Wise et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS