Scaled runge-kutta-nyström methods for the second order differential equationÿ=f(x,y)

DOI10.1080/00207168908803734zbMath0679.65051OpenAlexW2037372954WikidataQ115311116 ScholiaQ115311116MaRDI QIDQ4729258

Ch. Tsitouras, George Papageorgiou

Publication date: 1989

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207168908803734

zbMATH Keywords

computational efficiencysecond order differential equationsscaled Runge-Kutta-Nyström methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (8)

Continuous extensions to Nyström methods for second order initial value problems ⋮ Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors ⋮ A new optimized non-FSAL embedded Runge-Kutta-Nyström algorithm of orders 6 and 4 in six stages ⋮ Runge-Kutta interpolants based on values from two successive integration steps ⋮ On the efficiency of Runge-Kutta-Nyström methods with interpolants for solving equations of the form \(Y=F(T,Y,Y')\) over short timespans ⋮ Generalized Laguerre pseudospectral method based Laguerre interpolation ⋮ Continuous Runge-Kutta-Nyström methods for initial value problems with periodic solutions ⋮ Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations

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 \(y=f(x,y)\)
• Klassische Runge-Kutta-Nyström-Formeln mit SchrittweitenKontrolle für Differentialgleichungen \(\ddot x= f(t,x)\)
• Interpolation for Runge–Kutta Methods
• Eine Runge-Kutta-Nyström-Formel 9-ter Ordnung mit Schrittweitenkontrolle für Differentialgleichungenx =f(t, x)
• Interpolants for Runge-Kutta formulas
• Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
• [https://portal.mardi4nfdi.de/wiki/Publication:5678377 A Runge-Kutta Nystr�m algorithm]

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