Runge-Kutta interpolants for high precision computations

DOI10.1007/s11075-007-9104-4zbMath1120.65085OpenAlexW2029189338MaRDI QIDQ2641455

Ch. Tsitouras

Publication date: 20 August 2007

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

Full work available at URL: https://doi.org/10.1007/s11075-007-9104-4

zbMATH Keywords

numerical resultsinitial value problemRunge-Kutta pairsinterpolation methodsdense outputquadruple precision

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 (4)

The linear barycentric rational method for a class of delay Volterra integro-differential equations ⋮ Polynomial algebra for Birkhoff interpolants ⋮ Runge-Kutta pairs of order \(5(4)\) satisfying only the first column simplifying assumption ⋮ Bandlimited implicit Runge-Kutta integration for astrodynamics

Uses Software

• Mathematica
• nag
• NSDTST
• STDTST

Cites Work

• Runge-Kutta interpolants based on values from two successive integration steps
• Interpolating high-order Runge-Kutta formulas
• Runge-Kutta-Nyström triples
• High order embedded Runge-Kutta formulae
• A fifth-order interpolant for the Dormand and Prince Runge-Kutta method
• Symbolic derivation of Runge-Kutta order conditions
• Differentiable Interpolants for High-Order Runge–Kutta Methods
• Interpolation for Runge–Kutta Methods
• Practical Aspects of Interpolation in Runge-Kutta Codes
• Initial Value Routines in the NAG Library
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
• Generation of high-order interpolants for explicit Runge-Kutta pairs
• Interpolants for Runge-Kutta formulas
• Two FORTRAN packages for assessing initial value methods
• Runge-Kutta triples
• Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
• Comparing Numerical Methods for Ordinary Differential Equations
• Coefficients for the study of Runge-Kutta integration processes
• On Runge-Kutta processes of high order
• Implicit Runge-Kutta Processes
• Optimized explicit Runge-Kutta pair of orders \(9(8)\)
• Continuous approximation with embedded Runge-Kutta methods
• High-order explicit Runge-Kutta pairs with low stage order

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