An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems

DOI10.1016/j.cpc.2011.11.002zbMath1264.65111OpenAlexW2069787055MaRDI QIDQ1948845

A. A. Kosti, Zacharias A. Anastassi, Theodore E. Simos

Publication date: 25 April 2013

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

Full work available at URL: https://doi.org/10.1016/j.cpc.2011.11.002

zbMATH Keywords

numerical examplestwo-body probleminitial value problemsRunge-Kutta-Nyström methodsphase-lagexplicit methodslocal truncation errordissipative error

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Two-body problems (70F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

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Cites Work

• A \(P\)-stable eighth-order method for the numerical integration of periodic initial-value problems
• A phase-fitted Runge-Kutta-Nyström method for the numerical solution of initial value problems with oscillating solutions
• Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
• A \(5(3)\) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems
• Practical points concerning the solution of the Schrödinger equation
• Families of Runge-Kutta-Nystrom Formulae
• An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields
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