On symplectic and symmetric ARKN methods

DOI10.1016/j.cpc.2012.02.005zbMath1356.65243OpenAlexW2092175433MaRDI QIDQ1946119

Wei Shi, Xin-Yuan Wu

Publication date: 18 April 2013

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2012.02.005

zbMATH Keywords

symmetryoscillatory systemHamiltonian systemARKN integratorsoscillatory second-order initial value problemsadapted Runge-Kutta-Nyström methods (ARKN methods)symplecticness conditions

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (13)

Symplectic and symmetric trigonometrically-fitted ARKN methods ⋮ A note on symplectic and symmetric ARKN methods ⋮ A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems ⋮ The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two ⋮ Adapted Falkner-type methods solving oscillatory second-order differential equations ⋮ Approximate periodic solutions for oscillatory phenomena modelled by nonlinear differential equations ⋮ Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations ⋮ SYMPLECTIC RUNGE-KUTTA METHODS OF HIGH ORDER BASED ON W-TRANSFORMATION ⋮ Extended phase properties and stability analysis of RKN-type integrators for solving general oscillatory second-order initial value problems ⋮ Efficient energy-preserving integrators for oscillatory Hamiltonian systems ⋮ Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix ⋮ Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators ⋮ Multidimensional ARKN methods for general oscillatory second-order initial value problems

Cites Work

• Unnamed Item
• Unnamed Item
• Symmetric and symplectic exponentially fitted Runge-Kutta methods of high order
• Multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems
• Order conditions for ARKN methods solving oscillatory systems
• High-order P-stable multistep methods
• Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
• Geometric numerical integration by means of exponentially-fitted methods
• Trigonometrically-fitted ARKN methods for perturbed oscillators
• An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems
• Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions
• A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators
• Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
• New methods for oscillatory systems based on ARKN methods
• Solving Ordinary Differential Equations I
• Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems

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