Generating functions for dynamical systems with symmetries, integrals, and differential invariants

DOI10.1016/S0167-2789(97)00218-2zbMath1194.37089MaRDI QIDQ992236

Gilles Reinout Willem Quispel, Robert I. Mclachlan

Publication date: 11 September 2010

Published in: Physica D (Search for Journal in Brave)

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Poisson manifolds; Poisson groupoids and algebroids (53D17)

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Explicit volume-preserving and symplectic integrators for trigonometric polynomial flows., Dynamic programming and Lagrange multipliers for active relaxation of resources in nonlinear non-equilibrium systems, Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation, Volume-preserving integrators have linear error growth, Finite difference approximations and cosymmetry conservation in filtration-convection problem, Geometric integration of conservative polynomial ODEs, Invariants in separated variables: Yang-Baxter, entwining and transfer maps

Cites Work

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• Symplectic integration of Hamiltonian wave equations
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• Explicit Lie-Poisson integration and the Euler equations
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