Symplectic Runge-Kutta and related methods: Recent results

DOI10.1016/0167-2789(92)90245-IzbMath0779.58019OpenAlexW2050141483MaRDI QIDQ687818

Jesús María Sanz-Serna

Publication date: 28 November 1993

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

Full work available at URL: https://doi.org/10.1016/0167-2789(92)90245-i

zbMATH Keywords

Runge-Kuttasymplectic algorithms

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

Integrable discrete systems and numerical integrators, Composite symmetric general linear methods (COSY-GLMs) for the long-time integration of reversible Hamiltonian systems, Symplectic Hamiltonian finite element methods for electromagnetics, Development of an explicit non-staggered scheme for solving three-dimensional Maxwell's equations, New conservative gyrokinetic full-\(f\) Vlasov code and its comparison to gyrokinetic \(\delta f\) particle-in-cell code, Vlasov and Drift Kinetic Simulation Methods Based on the Symplectic Integrator, Conservative High-Order Time Integration for Lagrangian Hydrodynamics, A fourth-order AVF method for the numerical integration of sine-Gordon equation, Defect-controlled numerical methods and shadowing for chaotic differential equations, Development of a 3D staggered FDTD scheme for solving Maxwell's equations in Drude medium, Classification with Runge-Kutta networks and feature space augmentation, Discontinuous Galerkin methods with time-operators in their numerical traces for time-dependent electromagnetics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Order conditions for canonical Runge-Kutta-Nyström methods
• Fourth-order symplectic integration
• A scheme for the implementation of implicit Runge-Kutta methods
• A Hamiltonian, explicit algorithm with spectral accuracy for the `good' Boussinesq system
• A symplectic integration algorithm for separable Hamiltonian functions
• Runge-Kutta schemes for Hamiltonian systems
• Canonical Runge-Kutta methods
• Integrators for Lie-Poisson dynamical systems
• An easily implementable fourth-order method for the time integration of wave problems
• Long-time symplectic integration: the example of four-vortex motion
• Symplectic integration of Hamiltonian systems
• Tree graphs and the solution to the Hamilton–Jacobi equation
• Studies in Numerical Nonlinear Instability III: Augmented Hamiltonian Systems
• Order Conditions for Canonical Runge–Kutta Schemes
• An Explicit Runge–Kutta–Nyström Method is Canonical If and Only If Its Adjoint is Explicit
• Partitioned Runge-Kutta Methods for Separable Hamiltonian Problems
• Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods