Low order practical Runge-Kutta-Nyström methods

DOI10.1007/BF02278707zbMath0602.65044OpenAlexW1512474277MaRDI QIDQ1082044

J. M. Fine

Publication date: 1987

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02278707

zbMATH Keywords

error estimatesefficiencyRunge-Kutta-Nyström methodscomparisonssecond order systemtruncation error coefficients

Mathematics Subject Classification ID

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

Related Items

Interpolants for Runge-Kutta-Nyström methods ⋮ Natural continuous extension of Runge-Kutta methods for Volterra integrodiffential equations ⋮ Runge-Kutta-Nyström triples ⋮ Continuous parallel-iterated RKN-type PC methods for nonstiff IVPs ⋮ Some Nyström pairs for the general second-order initial-value problem ⋮ A contrast of direct and transformed Nyström pairs ⋮ Twostep-by-twostep continuous PIRKN-type PC methods for nonstiff IVPs ⋮ A computational procedure for interaction of high-speed vehicles on flexible structures without assuming known vehicle nominal motion ⋮ Runge-Kutta-Nyström methods for general second order ODEs with application to multi-body systems ⋮ Two-step-by-two-step PIRKN-type PC methods based on Gauss-Legendre collocation points for nonstiff IVPs ⋮ Parallel-iterated pseudo two-step Runge-Kutta-Nyström methods for nonstiff second-order IVPs

Uses Software

• NSDTST
• STDTST

Cites Work

• Stability of explicit Runge-Kutta methods
• Interpolants for Runge-Kutta-Nyström methods
• A family of embedded Runge-Kutta formulae
• Klassische Runge-Kutta-Nyström-Formeln mit Schrittweiten-Kontrolle für Differentialgleichungen \(\ddot x=f(t,x,\dot x)\)
• A theory for Nyström methods
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• Families of Direct Fourth-Order Methods for the Numerical Solution of General Second-Order Initial-Value-Problems
• The Stability of Numerical Methods for Second Order Ordinary Differential Equations
• Two FORTRAN packages for assessing initial value methods
• Zur Stabilität des Nyströmschen Verfahrens I
• Comparing Numerical Methods for Ordinary Differential Equations
• Zur Radizierung mit der Rechenmaschine