Geometric integration for the linear-gradient system

Computational methods for problems pertaining to mechanics of particles and systems (70-08) Numerical methods for initial value problems involving ordinary differential equations (65L05) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Cites Work

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Linear energy-preserving integrators for Poisson systems
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
Hamiltonian-conserving discrete canonical equations based on variational difference quotients
On quadratic invariants and symplectic structure
On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.
Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
The scalar auxiliary variable (SAV) approach for gradient flows
An efficient geometric method for incompressible hydrodynamics on the sphere
A new Lagrange multiplier approach for gradient flows
Finite-mode analogs of 2D ideal hydrodynamics: Coadjoint orbits and local canonical structure
Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation
Poisson integrators
Time integration and discrete Hamiltonian systems
Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
Stability of Runge-Kutta Methods for Trajectory Problems
Geometric integration using discrete gradients
Explicit Lie-Poisson integration and the Euler equations
A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation
Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables
Collective symplectic integrators
Free Energy of a Nonuniform System. I. Interfacial Free Energy
Collective Lie-Poisson integrators on R3
A Sixth Order Averaged Vector Field Method
A new class of energy-preserving numerical integration methods
Geometric Numerical Integration

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