NEURAL NETWORK-BASED DERIVATION OF EFFICIENT HIGH-ORDER RUNGE–KUTTA–NYSTRÖM PAIRS FOR THE INTEGRATION OF ORBITS

DOI10.1142/S0129183111016919zbMath1263.65069OpenAlexW1976402608MaRDI QIDQ4914208

Ioannis Th. Famelis

Publication date: 18 April 2013

Published in: International Journal of Modern Physics C (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129183111016919

zbMATH Keywords

neural networksnumerical examplesKepler problemdifferential evolutionorbital problemsRunge-Kutta-Nyström method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Orbital mechanics (70M20)

Cites Work

• Quaternions and the perturbed Kepler problem
• New embedded explicit pairs of exponentially fitted Runge-Kutta methods
• Differential evolution -- a simple and efficient heuristic for global optimization over continuous spaces
• A tenth-order symplectic Runge-Kutta-Nyström method
• Families of Runge-Kutta-Nystrom Formulae
• Solving Ordinary Differential Equations I
• High-Order Embedded Runge-Kutta-Nystrom Formulae
• High Phase-Lag-Order Runge--Kutta and Nyström Pairs
• Numerical Methods for Ordinary Differential Equations

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