Functional equivariance and modified vector fields
DOI10.3934/JCD.2023010MaRDI QIDQ6616285
Publication date: 9 October 2024
Published in: Journal of Computational Dynamics (Search for Journal in Brave)
backward error analysisgeometric numerical integrationmodified vector fieldsfunctional equivarianceinvariant preserving methods
Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)
Cites Work
- B-series methods are exactly the affine equivariant methods
- B-series methods cannot be volume-preserving
- Order conditions for numerical methods for partitioned ordinary differential equations
- Manifolds, tensor analysis, and applications.
- Canonical \(B\)-series
- On quadratic invariants and symplectic structure
- Prolongations of tensor fields and connections to tangent bundles. I: General theory
- Stability of Runge-Kutta Methods for Trajectory Problems
- Splitting methods
- Preserving first integrals and volume forms of additively split systems
- Symplectic Methods Based on Decompositions
- Geometric Numerical Integration
- B-Series
- Aromatic Butcher series
- Functional equivariance and conservation laws in numerical integration
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