A Symplectic Trigonometrically Fitted Modified Partitioned Runge-Kutta Method for the Numerical Integration of Orbital Problems

DOI10.1002/ANAC.200510037zbMath1084.65128OpenAlexW1996028789MaRDI QIDQ5717700

Th. Monovasilis, Zacharoula Kalogiratou, Theodore E. Simos

Publication date: 10 January 2006

Published in: Applied Numerical Analysis & Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/anac.200510037

zbMATH Keywords

two-body problemHamiltonian systemsharmonic oscillatortrigonometrically fitted methodsSymplectic integration

Mathematics Subject Classification ID

Two-body problems (70F05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Orbital mechanics (70M20) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Free motions in linear vibration theory (70J30)

Related Items (3)

Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods ⋮ Diagonally implicit trigonometrically fitted symplectic Runge-Kutta methods ⋮ Runge-Kutta type methods with special properties for the numerical integration of ordinary differential equations

Cites Work

• An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
• Exponentially-fitted explicit Runge-Kutta methods
• Stabilization of Cowell's method
• Extended One-Step Methods: An Exponential Fitting Approach
• The accuracy of symplectic integrators
• Exponentially-fitted algorithms: fixed or frequency dependent knot points?
• Effective Numerical Approximation of Schrödinger type Equations through Multiderivative Exponentially-fitted Schemes
• Efficient Numerical Solution of Orbital Problems with the use of Symmetric Four-step Trigonometrically-fitted Methods
• Non-existence of the modified first integral by symplectic integration methods

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