High order explicit Runge-Kutta Nyström pairs

DOI10.1007/s11075-012-9571-0zbMath1259.65120OpenAlexW2069437940MaRDI QIDQ1938087

Kevin R. Grazier, Mohammad A. Qureshi, Philip W. Sharp

Publication date: 1 February 2013

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-012-9571-0

zbMATH Keywords

efficiencynumerical comparisonshigh ordersecond-order initial value problemsdouble precision arithmeticexplicit Runge-Kutta Nyström pairs

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)

Related Items (1)

A new class of efficient one-step contractivity preserving high-order time discretization methods of order 5 to 14

Uses Software

• NSDTST
• STDTST

Cites Work

• New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form \(y=f(x,y)\)
• High order embedded Runge-Kutta formulae
• Solving Ordinary Differential Equations I
• N-body simulations
• High-Order Embedded Runge-Kutta-Nystrom Formulae
• Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
• High Phase-Lag-Order Runge--Kutta and Nyström Pairs
• Two FORTRAN packages for assessing initial value methods
• Unnamed Item

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