Optimal Error Estimates of SAV Crank–Nicolson Finite Element Method for the Coupled Nonlinear Schrödinger Equation

Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals

(2022) Tomoya Kemmochi et al.   BIT NUMERICAL MATHEMATICS

Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs

(2022) Dongfang Li et al.   MATHEMATICS OF COMPUTATION

Structure-preserving Gauss methods for the nonlinear Schrödinger equation

(2021) Georgios Akrivis et al.   CALCOLO

Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows

(2020) Hongtao Chen et al.   NUMERISCHE MATHEMATIK

Numerical solution of coupled nonlinear Schrödinger equations on unbounded domains

(2020) Hongwei Li et al.   APPLIED MATHEMATICS LETTERS

Mass- and energy-conserving difference schemes for nonlinear fractional Schrödinger equations

(2020) Xiaoxi Li et al.   APPLIED MATHEMATICS LETTERS

Linearly Implicit and High-Order Energy-Conserving Schemes for Nonlinear Wave Equations

(2020) Dongfang Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Energy stability and convergence of SAV block-centered finite difference method for gradient flows

(2019) Xiaoli Li et al.   MATHEMATICS OF COMPUTATION

Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations

(2019) Xiaobing Feng   Communications in Computational Physics

Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions

(2019) Wenjun Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs

(2019) Jiaxiang Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Energy-conserving methods for the nonlinear Schrödinger equation

(2018) L. Barletti et al.   APPLIED MATHEMATICS AND COMPUTATION

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen 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

An energy conservative difference scheme for the nonlinear fractional Schrödinger equations

(2015) Pengde Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical computations for N-coupled nonlinear Schrödinger equations by split step spectral methods

(2013) Shanshan Wang et al.   APPLIED MATHEMATICS AND COMPUTATION

Crank–Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative

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

A New Error Analysis of Crank–Nicolson Galerkin FEMs for a Generalized Nonlinear Schrödinger Equation

(2013) Jilu Wang   JOURNAL OF SCIENTIFIC COMPUTING

New conservative difference schemes for a coupled nonlinear Schrödinger system

(2009) Tingchun Wang et al.   APPLIED MATHEMATICS AND COMPUTATION

Multisymplectic integration of N-coupled nonlinear Schrödinger equation with destabilized periodic wave solutions

(2008) Ayhan Aydın   CHAOS SOLITONS & FRACTALS