Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods

DOI10.1007/BF01385510zbMath0735.65048MaRDI QIDQ5896696

Timo Eirola, Jesús María Sanz-Serna

Publication date: 1992

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133622

zbMATH Keywords

conservation lawsHamiltonian systemsmultistep methodssymplectic structureone-leg methods

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (13)

On quadratic invariants and symplectic structure ⋮ Block boundary value methods for linear Hamiltonian systems ⋮ On the relations between B\(_2\)VMs and Runge-Kutta collocation methods ⋮ Conjugate symplecticity of second-order linear multi-step methods ⋮ Symmetric second derivative integration methods ⋮ G-symplecticity implies conjugate-symplecticity of the underlying one-step method ⋮ Symplectic properties of multistep Runge-Kutta methods. ⋮ G-symplectic integration of many body problems ⋮ Symplectic Runge-Kutta and related methods: Recent results ⋮ Invariants and numerical methods for ODEs ⋮ Order conditions for canonical Runge-Kutta-Nyström methods ⋮ A note on symplecticity of step-transition mappings for multi-step methods ⋮ Symmetric schemes, time reversal symmetry and conservative methods for Hamiltonian systems

Cites Work

• A Hamiltonian, explicit algorithm with spectral accuracy for the `good' Boussinesq system
• Runge-Kutta schemes for Hamiltonian systems
• On the equivalence of \(A\)-stability and \(G\)-stability
• Convergence analysis of one-step schemes in the method of lines
• Canonical Runge-Kutta methods
• G-stability is equivalent toA-stability
• On One-Leg Multistep Methods
• Symplectic integration of Hamiltonian systems
• Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
• Studies in Numerical Nonlinear Instability III: Augmented Hamiltonian Systems
• Order Conditions for Canonical Runge–Kutta Schemes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods