Continuous extensions to high order runge-kutta methods

DOI10.1080/00207169708804616zbMath0891.65088OpenAlexW2158439065MaRDI QIDQ4375404

Ch. Tsitouras, George Papageorgiou

Publication date: 3 July 1998

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

Full work available at URL: https://doi.org/10.1080/00207169708804616

zbMATH Keywords

systemsnumerical resultserror analysisscalingRunge-Kutta methodsHermite interpolationnonstiff initial value problems

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) Error bounds for numerical methods for ordinary differential equations (65L70)

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Uses Software

• nag

Cites Work

• Runge-Kutta interpolants based on values from two successive integration steps
• Interpolating high-order Runge-Kutta formulas
• A family of embedded Runge-Kutta formulae
• High order embedded Runge-Kutta formulae
• A fifth-order interpolant for the Dormand and Prince Runge-Kutta method
• 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
• Explicit Runge–Kutta Methods with Estimates of the Local Truncation Error
• Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
• 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

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