# Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations

@inproceedings{Hairer2004GeometricNI, title={Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations}, author={Ernst Hairer and Christian Lubich and Gerhard Wanner}, year={2004} }

## 3,202 Citations

Important Aspects of Geometric Numerical Integration

- PhysicsJ. Sci. Comput.
- 2005

Using a modulated Fourier expansion, much insight can be gained for methods applied to problems where the high oscillations stem from a linear part of the vector field and where only one (or a few) high frequencies are present.

On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: Energy conservation and multi-symplecticity

- MathematicsJ. Comput. Phys.
- 2020

Numerical integration of variational equations.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is found that the best numerical performance is exhibited by the "tangent map method," a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy.

Backward error analysis for conjugate symplectic methods

- Mathematics
- 2022

This work shows how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures systematically, provided that a variational formulation of the method is known.

A review of some geometric integrators

- MathematicsAdv. Model. Simul. Eng. Sci.
- 2018

The Discrete Exterior Calculus, which is a structure-preserving integrator based on differential geometry and exterior calculus, is presented, which leads to numerical schemes which preserve exactly the energy of the system.

Study of geometric integrators for differential equations

- Mathematics
- 2008

The aim of the work described in this thesis is the construction and the study of structure-preserving numerical integrators for differential equations, which share some geometric properties of theâ€¦

Para-Hamiltonian form for General Autonomous ODE Systems: Introductory Results

- MathematicsEntropy
- 2022

We propose a new tool to deal with autonomous ODE systems for which the solution to the Hamiltonian inverse problem is not available in the usual, classical sense. Our approach allows a class ofâ€¦

Discrete Integrable Systems and Geometric Numerical Integration

- Mathematics
- 2018

This thesis deals with discrete integrable systems theory and modified Hamiltonian equations in the field of geometric numerical integration. Modified Hamiltonians are used to show that symplecticâ€¦

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