B-stability of numerical integrators on Riemannian manifolds
DOI10.3934/jcd.2024002arXiv2308.08261OpenAlexW4390949562WikidataQ129792404 ScholiaQ129792404MaRDI QIDQ6120391
No author found.
Publication date: 20 February 2024
Published in: Journal of Computational Dynamics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2308.08261
Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Ordinary differential equations and systems on manifolds (34C40) Manifolds of metrics (especially Riemannian) (58D17) Computational methods for problems pertaining to differential geometry (53-08)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- High-order symplectic partitioned Lie group methods
- Lie group spectral variational integrators
- An introduction to Lie group integrators - basics, new developments and applications
- Riemannian geometry and matrix geometric means
- Riemannian geometry for the statistical analysis of diffusion tensor data
- On the dynamics in space of rods undergoing large motions - A geometrically exact approach
- High order Runge-Kutta methods on manifolds
- Numerical integration of ordinary differential equations on manifolds
- Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups
- A symplectic integrator for Riemannian manifolds
- Galerkin Lie-group variational integrators based on unit quaternion interpolation
- Time integration of rigid bodies modelled with three rotation parameters
- RATTLie: a variational Lie group integration scheme for constrained mechanical systems
- Convergence of Lie group integrators
- Riemannian cubics and elastica in the manifold \(\operatorname{SPD}(n)\) of all \(n\times n\) symmetric positive-definite matrices
- Discrete variational Lie group formulation of geometrically exact beam dynamics
- Singularity-free time integration of rotational quaternions using non-redundant ordinary differential equations
- Lie group variational integrators for the full body problem
- Contraction theory on Riemannian manifolds
- Convergence of the generalized-\(\alpha\) scheme for constrained mechanical systems
- Global Gronwall estimates for integral curves on Riemannian manifolds
- Error analysis of generalized-\(\alpha\) Lie group time integration methods for constrained mechanical systems
- A Riemannian framework for tensor computing
- A minimal-variable symplectic integrator on spheres
- Topics in structure-preserving discretization
- Discrete mechanics and variational integrators
- A stability property of implicit Runge-Kutta methods
- Riemannian center of mass and mollifier smoothing
- Dissipative Numerical Schemes on Riemannian Manifolds with Applications to Gradient Flows
- Introduction to Riemannian Manifolds
- A Class of Intrinsic Schemes for Orthogonal Integration
- Lie group integrators for mechanical systems
- Energy-preserving methods on Riemannian manifolds
- A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
- Adjoint and selfadjoint Lie-group methods
- Non-Euclidean Contraction Theory for Robust Nonlinear Stability
This page was built for publication: B-stability of numerical integrators on Riemannian manifolds