The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods
DOI10.1016/j.cam.2022.114964zbMath1502.65043OpenAlexW4309930262MaRDI QIDQ2112698
Publication date: 11 January 2023
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114964
multi-frequency oscillatory Hamiltonian systemsfree-tree theorysymplectic ERKN methodstri-coloured SSEN-rooted-tree theory
Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
Cites Work
- Unnamed Item
- A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems
- ERKN methods for long-term integration of multidimensional orbital problems
- A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems
- ERKN integrators for systems of oscillatory second-order differential equations
- Order conditions for canonical Runge-Kutta-Nyström methods
- Almost symplectic Runge-Kutta schemes for Hamiltonian systems
- Extended RKN-type methods for numerical integration of perturbed oscillators
- Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
- A symplectic integration algorithm for separable Hamiltonian functions
- Trigonometrically-fitted ARKN methods for perturbed oscillators
- Runge-Kutta schemes for Hamiltonian systems
- A numerical algorithm for Hamiltonian systems
- An easily implementable fourth-order method for the time integration of wave problems
- Canonical Runge-Kutta-Nyström methods of orders five and six
- A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation
- Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods
- Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix
- A Gautschi-type method for oscillatory second-order differential equations
- Two-step extended RKN methods for oscillatory systems
- Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems
- Exponentially-fitted explicit Runge-Kutta methods
- Bounds on asymptotic-numerical solvers for ordinary differential equations with extrinsic oscillation
- Efficient energy-preserving integrators for oscillatory Hamiltonian systems
- Novel improved multidimensional Störmer-Verlet formulas with applications to four aspects in scientific computation
- Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations
- An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems
- Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations
- Order conditions for RKN methods solving general second-order oscillatory systems
- Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
- Solving Ordinary Differential Equations I
- The canonicity of mappings generated by Runge-Kutta type methods when integrating the systems
- Symplectic Geometric Algorithms for 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
- High-Order Symplectic Runge–Kutta–Nyström Methods
- Structure-Preserving Algorithms for Oscillatory Differential Equations
- Explicit, Time Reversible, Adaptive Step Size Control
- Geometric integrators for ODEs
- Geometric Numerical Integration
- Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems
This page was built for publication: The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods
