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

Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

(2020) Zhaojie Zhou   Numerical Mathematics-Theory Methods and Applications

Energy and entropy preserving numerical approximations of thermodynamically consistent crystal growth models

(2019) Jun Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

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

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

High-order energy-conserving Line Integral Methods for charged particle dynamics

(2019) Luigi Brugnano 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

A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator

(2018) Luigi Brugnano et al.   Communications in Nonlinear Science and Numerical Simulation

The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations

(2018) Bin Wang et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

The scalar auxiliary variable (SAV) approach for gradient flows

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

Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach

(2018) Qing Cheng et al.   JOURNAL OF SCIENTIFIC COMPUTING

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

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

Fractional magneto-hydrodynamics: Algorithms and applications

(2018) Fangying Song et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Optimal Superconvergence of Energy Conserving Local Discontinuous Galerkin Methods for Wave Equations

(2016) Waixiang Cao et al.   Communications in Computational Physics

An energy-conserving second order numerical scheme for nonlinear hyperbolic equation with an exponential nonlinear term

(2015) Lingdi Wang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Energy-conserving dissipative particle dynamics with temperature-dependent properties

(2014) Zhen Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The minimal stage, energy preserving Runge–Kutta method for polynomial Hamiltonian systems is the averaged vector field method

(2014) Elena Celledoni et al.   MATHEMATICS OF COMPUTATION

Discrete gradient methods have an energy conservation law

(2013) Robert I. McLachlan et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Efficient energy-preserving integrators for oscillatory Hamiltonian systems

(2012) Xinyuan Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Energy-preserving Runge-Kutta methods

(2009) Elena Celledoni et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Soliton perturbation theory for phi-four model and nonlinear Klein–Gordon equations

(2008) Ryan Sassaman et al.   Communications in Nonlinear Science and Numerical Simulation

A new class of energy-preserving numerical integration methods

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

New travelling wave solutions to the Boussinesq and the Klein–Gordon equations

(2006) Abdul-Majid Wazwaz   Communications in Nonlinear Science and Numerical Simulation