What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration

DOI10.1088/0951-7715/14/6/315zbMath0994.65138OpenAlexW2052857132WikidataQ126011193 ScholiaQ126011193MaRDI QIDQ2758133

Robert I. Mclachlan, Gilles Reinout Willem Quispel

Publication date: 29 September 2002

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/7d829d756c2da410bfc5e94478ee66ae8e674938

zbMATH Keywords

classificationdynamical systemsnumerical examplesflowgeometric integrationsymplectic integratorgroup of diffeomorphismsLie pseudogroupsLie group integrator

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (18)

Multi-conformal-symplectic PDEs and discretizations ⋮ Volume preservation by Runge-Kutta methods ⋮ Numerical methods for non conservative perturbations of conservative problems ⋮ Metriplectic structure, Leibniz dynamics and dissipative systems ⋮ Second order conformal symplectic schemes for damped Hamiltonian systems ⋮ Functional equivariance and conservation laws in numerical integration ⋮ Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces ⋮ Derivation of symmetric composition constants for symmetric integrators ⋮ Structure-preserving Exponential Runge--Kutta Methods ⋮ Euler-Poincaré flows and Leibniz structure of nonlinear reaction-diffusion type systems ⋮ Exponential integrators based on discrete gradients for linearly damped/driven Poisson systems ⋮ B-series methods are exactly the affine equivariant methods ⋮ Conformal Hamiltonian systems ⋮ Differential invariant algebras of Lie pseudo-groups ⋮ Preface. Special issue in honor of Reinout Quispel ⋮ Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations ⋮ Stochastic conformal schemes for damped stochastic Klein-Gordon equation with additive noise ⋮ Hybrid solvers for composition and splitting methods

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