Exponential integrator preserving mass boundedness and energy conservation for nonlinear Schrödinger equation

A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions

(2020) Chaolong Jiang et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

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

(2020) Jin Cui et al.   APPLIED MATHEMATICS LETTERS

Geometric Exponential Integrators

(2019) Xuefeng Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A linearized energy–conservative finite element method for the nonlinear Schrödinger equation with wave operator

(2019) Wentao Cai et al.   APPLIED NUMERICAL MATHEMATICS

A Linearly Implicit and Local Energy-Preserving Scheme for the Sine-Gordon Equation Based on the Invariant Energy Quadratization Approach

(2019) Chaolong Jiang et al.   JOURNAL OF SCIENTIFIC COMPUTING

Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrödinger equation

(2019) Tingchun Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation

(2018) Jialin Hong et al.   APPLIED NUMERICAL MATHEMATICS

The scalar auxiliary variable (SAV) approach for gradient flows

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

Partitioned averaged vector field methods

(2018) Wenjun Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Unconditional convergence of linearized implicit finite difference method for the 2D/3D Gross-Pitaevskii equation with angular momentum rotation

(2018) Tingchun Wang et al.   Science China-Mathematics

Symplectic exponential Runge–Kutta methods for solving nonlinear Hamiltonian systems

(2017) Lijie Mei et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

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

A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation

(2017) Yuezheng Gong et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Structure-preserving Exponential Runge--Kutta Methods

(2017) Ashish Bhatt et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems

(2016) Yu-Wen Li et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Two Energy-Conserved Splitting Methods for Three-Dimensional Time-Domain Maxwell's Equations and the Convergence Analysis

(2015) Jiaxiang Cai et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Energy Conserving Local Discontinuous Galerkin Methods for the Nonlinear Schrödinger Equation with Wave Operator

(2014) Li Guo et al.   JOURNAL OF SCIENTIFIC COMPUTING

Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions

(2013) Tingchun Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator

(2012) Weizhu Bao et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Semi-explicit symplectic partitioned Runge–Kutta Fourier pseudo-spectral scheme for Klein–Gordon–Schrödinger equations

(2010) Linghua Kong et al.   COMPUTER PHYSICS COMMUNICATIONS

Exponential integrators

(2010) Marlis Hochbruck et al.   ACTA NUMERICA

A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients

(2009) Mehdi Dehghan et al.   COMPUTER PHYSICS COMMUNICATIONS

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

A new class of energy-preserving numerical integration methods

(2008) G R W Quispel et al.   Journal of Physics A-Mathematical and Theoretical

Numerical methods for computing the ground state of spin-1 Bose-Einstein condensates in a uniform magnetic field

(2008) Fong Yin Lim et al.   PHYSICAL REVIEW E