On quadratic invariants and symplectic structure

DOI10.1007/BF01935643zbMath0813.65102MaRDI QIDQ1338532

Pavel B. Bochev, Clint Scovel

Publication date: 28 May 1995

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemsquadratic invariantssymplectic Runge-Kutta methodsnumerical flow

Mathematics Subject Classification ID

Hamilton's equations (70H05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (16)

Quadratic invariants and multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs ⋮ Adaptive, second-order, unconditionally stable partitioned method for fluid-structure interaction ⋮ Approximate preservation of quadratic first integrals by explicit Runge-Kutta methods ⋮ Monotonicity of quadratic forms with symplectic Runge-Kutta methods ⋮ Conjugate symplecticity of second-order linear multi-step methods ⋮ Refactorization of the midpoint rule ⋮ Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems ⋮ Functional equivariance and conservation laws in numerical integration ⋮ Symplectic Hamiltonian HDG methods for wave propagation phenomena ⋮ Symplectic properties of multistep Runge-Kutta methods. ⋮ Structure preservation of exponentially fitted Runge-Kutta methods ⋮ Structure-preserving Exponential Runge--Kutta Methods ⋮ Unnamed Item ⋮ An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants ⋮ B-series methods are exactly the affine equivariant methods ⋮ Symplectic Runge--Kutta Schemes for Adjoint Equations, Automatic Differentiation, Optimal Control, and More

Cites Work

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• Recent progress in the theory and application of symplectic integrators
• Runge-Kutta schemes for Hamiltonian systems
• Canonical Runge-Kutta methods
• Stability of Runge-Kutta Methods for Trajectory Problems
• Non-linear stability of a general class of differential equation methods
• Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods

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