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Hong Zhang et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2020)
Arbitrarily high-order linear energy stable schemes for gradient flow models
Yuezheng Gong et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2020)
A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
Chaolong Jiang et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2020)
Efficient energy-preserving scheme of the three-coupled nonlinear Schrodinger equation
Linghua Kong et al.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2019)
Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schrodinger Equations
Xiaobing Feng et al.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS (2019)
Geometric exponential integrators
Xuefeng Shen et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2019)
ENERGY-DECAYING EXTRAPOLATED RK-SAV METHODS FOR THE ALLEN-CAHN AND CAHN-HILLIARD EQUATIONS
Georgios Akrivis et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING (2019)
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
Jie Shen et al.
SIAM REVIEW (2019)
ENERGY STABILITY AND ERROR ESTIMATES OF EXPONENTIAL TIME DIFFERENCING SCHEMES FOR THE EPITAXIAL GROWTH MODEL WITHOUT SLOPE SELECTION
Lili Ju et al.
MATHEMATICS OF COMPUTATION (2018)
An energy-preserving Crank-Nicolson Galerkin spectral element method for the two dimensional nonlinear Schrodinger equation
Haochen Li et al.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2018)
The scalar auxiliary variable (SAV) approach for gradient flows
Jie Shen et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2018)
Stabilized Predictor-Corrector Schemes for Gradient Flows with Strong Anisotropic Free Energy
Jie Shen et al.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS (2018)
Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
Xiaofeng Yang et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2017)
A conservative Fourier pseudo-spectral method for the nonlinear Schrodinger equation
Yuezheng Gong et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2017)
A CHARACTERIZATION OF ENERGY-PRESERVING METHODS AND THE CONSTRUCTION OF PARALLEL INTEGRATORS FOR HAMILTONIAN SYSTEMS
Yuto Miyatake et al.
SIAM JOURNAL ON NUMERICAL ANALYSIS (2016)
EXPONENTIAL INTEGRATORS PRESERVING FIRST INTEGRALS OR LYAPUNOV FUNCTIONS FOR CONSERVATIVE OR DISSIPATIVE SYSTEMS
Yu-Wen Li et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING (2016)
GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations II: Dynamics and stochastic simulations
Xavier Antoine et al.
COMPUTER PHYSICS COMMUNICATIONS (2015)
General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs
Yu-Wen Li et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2015)
Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs
Yuezheng Gong et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2014)
Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations
Xavier Antoine et al.
COMPUTER PHYSICS COMMUNICATIONS (2013)
Fourth-order compact and energy conservative difference schemes for the nonlinear Schrodinger equation in two dimensions
Tingchun Wang et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2013)
MATHEMATICAL THEORY AND NUMERICAL METHODS FOR BOSE-EINSTEIN CONDENSATION
Weizhu Bao et al.
KINETIC AND RELATED MODELS (2013)
Preserving energy resp dissipation in numerical PDEs using the Average Vector Field method
E. Celledoni et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2012)
UNIFORM ERROR ESTIMATES OF FINITE DIFFERENCE METHODS FOR THE NONLINEAR SCHRODINGER EQUATION WITH WAVE OPERATOR
Weizhu Bao et al.
SIAM JOURNAL ON NUMERICAL ANALYSIS (2012)
Linear energy-preserving integrators for Poisson systems
David Cohen et al.
BIT NUMERICAL MATHEMATICS (2011)
A GENERAL FRAMEWORK FOR DERIVING INTEGRAL PRESERVING NUMERICAL METHODS FOR PDES
Morten Dahlby et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING (2011)
A new class of energy-preserving numerical integration methods
G. R. W. Quispel et al.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2008)
Symmetric exponential integrators with an application to the cubic Schrodinger equation
Elena Celledoni et al.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS (2008)
On the preservation of invariants by explicit Runge-Kutta methods
M. Calvo et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING (2006)
Kolmogorov spectrum of superfluid turbulence: Numerical analysis of the Gross-Pitaevskii equation with a small-scale dissipation
M Kobayashi et al.
PHYSICAL REVIEW LETTERS (2005)
Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
T Matsuo et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2001)
Symmetric projection methods for differential equations on manifolds
E Hairer
BIT NUMERICAL MATHEMATICS (2000)