A fifth-order interpolant for the Dormand and Prince Runge-Kutta method

DOI10.1016/0377-0427(90)90198-9zbMath0687.65078OpenAlexW2021910005MaRDI QIDQ1263257

Luis Rández, Juan I. Montijano, Manuel Calvo

Publication date: 1990

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(90)90198-9

zbMATH Keywords

solutionnumerical experimentsRunge-Kutta methodslocal truncation errorfifth-orderfifth-order interpolantsnonstiff DETEST problemsRunge-Kutta pair RK5(4)7M

Mathematics Subject Classification ID

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

Related Items (16)

A polyvalent Runge-Kutta triple ⋮ A new method for derivation of continuous Runge-Kutta formulas ⋮ Revealing hidden dynamics from time-series data by ODENet ⋮ Interpolating Runge-Kutta methods for vanishing delay differential equations ⋮ Runge-Kutta interpolants for high precision computations ⋮ Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors ⋮ Dense output for extrapolation methods ⋮ Bandlimited implicit Runge-Kutta integration for astrodynamics ⋮ Continuous extensions to high order runge-kutta methods ⋮ Multistep natural continuous extensions of Runge-Kutta methods: The potential for stable interpolation ⋮ The Josephson junction circuit family: network theory ⋮ Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels ⋮ Continuous approximation with embedded Runge-Kutta methods ⋮ A new embedded pair of Runge-Kutta formulas of orders 5 and 6 ⋮ Interpolants for Runge-Kutta pairs of order four and five ⋮ Optimal residuals and the Dahlquist test problem

Uses Software

• dverk
• DEPAC

Cites Work

• Unnamed Item
• A family of embedded Runge-Kutta formulae
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• Interpolation for Runge–Kutta Methods
• Some Practical Runge-Kutta Formulas
• Practical Aspects of Interpolation in Runge-Kutta Codes
• A Theoretical Criterion for Comparing Runge–Kutta Formulas
• Interpolants for Runge-Kutta formulas
• Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
• Comparing Numerical Methods for Ordinary Differential Equations
• Comparing Error Estimators for Runge-Kutta Methods

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