Runge-Kutta Pairs For Scalar Autonomous Initial Value Problems

DOI10.1080/00207160304669zbMath1018.65095OpenAlexW2006232429MaRDI QIDQ4805934

Ch. Tsitouras, George Papageorgiou

Publication date: 11 September 2003

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

Full work available at URL: https://doi.org/10.1080/00207160304669

zbMATH Keywords

numerical exampleserror boundsinitial value problemsRunge-Kutta methodsorder conditionsRunge-Kutta pairs

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) 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)

Related Items (2)

Symbolic derivation of Runge-Kutta order conditions ⋮ Isomeric trees and the order of Runge-Kutta methods

Cites Work

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• A family of embedded Runge-Kutta formulae
• Highly Continuous Interpolants for One-Step ODE Solvers and their Application to Runge--Kutta Methods
• Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
• Cheap Error Estimation for Runge--Kutta Methods
• High Phase-Lag-Order Runge--Kutta and Nyström Pairs
• Two FORTRAN packages for assessing initial value methods
• A General Family of Explicit Runge–Kutta Pairs of Orders $6(5)$
• On Runge-Kutta processes of high order

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