Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables

Relaxation Runge–Kutta Methods for Hamiltonian Problems

(2020) Hendrik Ranocha et al.   JOURNAL OF SCIENTIFIC COMPUTING

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen 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

Reprint of Analysis of Hamiltonian Boundary Value Methods (HBVMs): A class of energy-preserving Runge–Kutta methods for the numerical solution of polynomial Hamiltonian systems

(2015) Luigi Brugnano et al.   Communications in Nonlinear Science and Numerical Simulation

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

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

An energy-preserving exponentially-fitted continuous stage Runge–Kutta method for Hamiltonian systems

(2014) Yuto Miyatake   BIT NUMERICAL MATHEMATICS

Projection methods and discrete gradient methods for preserving first integrals of ODEs

(2014) Richard A. Norton et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

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

(2014) Yuezheng Gong 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

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

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

A General Framework for Deriving Integral Preserving Numerical Methods for PDEs

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

Energy-preserving Runge-Kutta methods

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

A new class of energy-preserving numerical integration methods

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