Geometry-preserving numerical methods for physical systems with finite-dimensional Lie algebras

DOI10.1007/s00332-023-10000-8arXiv2308.00820MaRDI QIDQ6185865

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Publication date: 30 January 2024

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2308.00820

zbMATH Keywords

discrete differential geometrydiscretization methods and integratorsgeometric methods in ODEs

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Numerical methods for initial value problems involving ordinary differential equations (65L05) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Discrete differential geometry (53A70)

Cites Work

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• A Lie systems approach to the Riccati hierarchy and partial differential equations
• High order Runge-Kutta methods on manifolds
• Runge-Kutta methods on Lie groups
• Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
• Improved high order integrators based on the Magnus expansion
• Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
• From constants of motion to superposition rules for Lie–Hamilton systems
• Lie systems: theory, generalisations, and applications
• Solving Ordinary Differential Equations I
• The Jordan–Schwinger representations of Cayley–Klein groups. I. The orthogonal groups
• Casimir invariants for the complete family of quasisimple orthogonal algebras
• On the solution of linear differential equations in Lie groups
• Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
• Quantum structure of the motion groups of the two-dimensional Cayley-Klein geometries
• Lie Algebras of Vector Fields in the Real Plane
• Conformal symmetries of spacetimes
• Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry
• Lie–Hamilton systems on curved spaces: a geometrical approach
• Nonlinear Complementary Filters on the Special Orthogonal Group
• A Guide to Lie Systems with Compatible Geometric Structures
• Lie Groups, Lie Algebras, and Representations
• Geometric Numerical Integration
• A global formulation of the Lie theory of transformation groups
• On the exponential solution of differential equations for a linear operator
• Reduction of time-dependent systems admitting a superposition principle
• Time symmetry and high-order Magnus methods

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