Linear High-Order Energy-Preserving Schemes for the Nonlinear Schrödinger Equation with Wave Operator Using the Scalar Auxiliary Variable Approach

Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models

(2020) Yuezheng Gong et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A conservative sine pseudo-spectral-difference method for multi-dimensional coupled Gross–Pitaevskii equations

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

Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation

(2020) Chaolong Jiang et al.   APPLIED NUMERICAL MATHEMATICS

Two novel classes of linear high-order structure-preserving schemes for the generalized nonlinear Schrödinger equation

(2020) Xin Li et al.   APPLIED MATHEMATICS LETTERS

Arbitrarily high-order linear energy stable schemes for gradient flow models

(2020) Yuezheng Gong et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Energy-stable Runge–Kutta schemes for gradient flow models using the energy quadratization approach

(2019) Yuezheng Gong et al.   APPLIED MATHEMATICS LETTERS

Novel high-order energy-preserving diagonally implicit Runge–Kutta schemes for nonlinear Hamiltonian ODEs

(2019) Hong Zhang et al.   APPLIED MATHEMATICS LETTERS

The scalar auxiliary variable (SAV) approach for gradient flows

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

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

(2018) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

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 Sixth order Averaged Vector Field Method

(2016) Haochen Li et al.   JOURNAL OF COMPUTATIONAL MATHEMATICS

Improving the accuracy of convexity splitting methods for gradient flow equations

(2016) Karl Glasner et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Functionally Fitted Energy-Preserving Methods for Solving Oscillatory Nonlinear Hamiltonian Systems

(2016) Yu--Wen Li et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation

(2016) Yuezheng Gong et al.   Communications in Computational Physics

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

(2014) Li Guo 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

Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator

(2010) Shanshan Wang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse

(2010) Weizhu Bao et al.   PHYSICA D-NONLINEAR PHENOMENA

A new class of energy-preserving numerical integration methods

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