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

Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation

(2020) Xiaoli Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

A second order unconditionally stable scheme for the modified phase field crystal model with elastic interaction and stochastic noise effect

(2020) Binhu Xia et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation

(2019) Qi Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

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

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

Numerical approximation of the fractional Cahn-Hilliard equation by operator splitting method

(2019) Shuying Zhai et al.   NUMERICAL ALGORITHMS

Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation

(2019) Zhengguang Liu et al.   NUMERICAL ALGORITHMS

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

A second-order, uniquely solvable, energy stable BDF numerical scheme for the phase field crystal model

(2018) Qi Li et al.   APPLIED NUMERICAL MATHEMATICS

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

(2017) Xiaofeng Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

On the Operator Splitting and Integral Equation Preconditioned Deferred Correction Methods for the “Good” Boussinesq Equation

(2017) Cheng Zhang et al.   JOURNAL OF SCIENTIFIC COMPUTING

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

Fast explicit operator splitting method and time-step adaptivity for fractional non-local Allen–Cahn model

(2016) Shuying Zhai et al.   APPLIED MATHEMATICAL MODELLING

Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach

(2016) Jia Zhao et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Fast and stable explicit operator splitting methods for phase-field models

(2015) Yuanzhen Cheng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

First and second order operator splitting methods for the phase field crystal equation

(2015) Hyun Geun Lee et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Characterizing solute segregation and grain boundary energy in binary alloy phase field crystal models

(2013) Jonathan Stolle et al.   COMPUTATIONAL MATERIALS SCIENCE

Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation

(2013) Arvind Baskaran et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

(2013) A. Baskaran et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

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

Stability and Convergence Analysis of Fully Discrete Fourier Collocation Spectral Method for 3-D Viscous Burgers’ Equation

(2012) Sigal Gottlieb et al.   JOURNAL OF SCIENTIFIC COMPUTING

Defect stability in phase-field crystal models: Stacking faults and partial dislocations

(2012) Joel Berry et al.   PHYSICAL REVIEW B

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

(2012) Mechthild Thalhammer   SIAM JOURNAL ON NUMERICAL ANALYSIS

Long Time Stability of a Classical Efficient Scheme for Two-dimensional Navier–Stokes Equations

(2012) S. Gottlieb et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

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

(2011) C. Wang et al.   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

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

A Generalized-Laguerre–Fourier–Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose–Einstein Condensates

(2009) Weizhu Bao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

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

(2008) Christian Lubich   MATHEMATICS OF COMPUTATION