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

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

Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein–Gordon equations

(2017) Changying Liu 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

Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method

(2017) Xiaofeng Yang et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

An efficient finite difference scheme for the 2D sine-Gordon equation

(2017) Xiaorong Kang et al.   Journal of Nonlinear Sciences and Applications

General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs

(2015) Yu-Wen Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

New explicit multi-symplectic scheme for nonlinear wave equation

(2014) Hao-chen Li et al.   APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION

Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs

(2014) Yuezheng Gong et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system

(2013) Jiaxiang Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method

(2012) E. Celledoni et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical simulation of two-dimensional sine-Gordon solitons by differential quadrature method

(2011) Ram Jiwari et al.   COMPUTER PHYSICS COMMUNICATIONS

A General Framework for Deriving Integral Preserving Numerical Methods for PDEs

(2011) Morten Dahlby et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)

(2009) Mehdi Dehghan et al.   COMPUTER PHYSICS COMMUNICATIONS

Symplectic wavelet collocation method for Hamiltonian wave equations

(2009) Huajun Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Dispersive properties of multisymplectic integrators

(2008) C.M. Schober et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

(2008) Mehdi Dehghan et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

Local structure-preserving algorithms for partial differential equations

(2008) YuShun Wang et al.   Science in China. Series A, Mathematics, physics, astronomy