A high order operator splitting method based on spectral deferred correction for the nonlocal viscous Cahn-Hilliard equation

Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation

(2021) Shuying Zhai et al.   JOURNAL OF SCIENTIFIC COMPUTING

Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models

(2020) Xiaochuan Tian et al.   SIAM REVIEW

Nonlocal-to-Local Convergence of Cahn–Hilliard Equations: Neumann Boundary Conditions and Viscosity Terms

(2020) Elisa Davoli et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn–Hilliard equation

(2020) Xiao Li et al.   MATHEMATICS OF COMPUTATION

The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation

(2020) Zhengguang Liu et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

A family of second-order energy-stable schemes for Cahn–Hilliard type equations

(2019) Zhiguo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Error Analysis and Numerical Simulations of Strang Splitting Method for Space Fractional Nonlinear Schrödinger Equation

(2019) Shuying Zhai et al.   JOURNAL OF SCIENTIFIC COMPUTING

Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation

(2019) Zhengguang Liu et al.   APPLIED NUMERICAL MATHEMATICS

Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation

(2018) Qiang Du et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient linear schemes for the nonlocal Cahn–Hilliard equation of phase field models

(2018) Xiaofeng Yang et al.   COMPUTER PHYSICS COMMUNICATIONS

Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations

(2017) Ruihan Guo et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

(2017) Qiang Du et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The nonlocal Cahn–Hilliard equation with singular potential: Well-posedness, regularity and strict separation property

(2017) Ciprian G. Gal et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations

(2017) Zhen Guan et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Convergence of a Fast Explicit Operator Splitting Method for the Epitaxial Growth Model with Slope Selection

(2017) Xiao Li et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

One-dimensional solutions of non-local Allen–Cahn-type equations with rough kernels

(2016) Matteo Cozzi et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations

(2016) Qiang Du et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Long Time Numerical Simulations for Phase-Field Problems Using $p$-Adaptive Spectral Deferred Correction Methods

(2015) Xinlong Feng et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Second order convex splitting schemes for periodic nonlocal Cahn–Hilliard and Allen–Cahn equations

(2014) Zhen Guan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2014) Zhen Guan et al.   NUMERISCHE MATHEMATIK

Error Analysis of the Strang Time-Splitting Laguerre–Hermite/Hermite Collocation Methods for the Gross–Pitaevskii Equation

(2012) Jie Shen et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations

(2012) Mechthild Thalhammer   SIAM JOURNAL ON NUMERICAL ANALYSIS

On stability of numerical schemes via frozen coefficients and the magnetic induction equations

(2010) Siddhartha Mishra et al.   BIT NUMERICAL MATHEMATICS

On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations

(2008) Christian Lubich   MATHEMATICS OF COMPUTATION