Symbolic derivation of Runge-Kutta order conditions

DOI10.1016/j.jsc.2003.07.001zbMath1137.65380OpenAlexW2018739671MaRDI QIDQ2643511

Ch. Tsitouras, Ioannis Th. Famelis, S. N. Papakostas

Publication date: 24 August 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2003.07.001

zbMATH Keywords

partitionsrooted treescombinatorial mathematics

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Uses Software

• Mathematica
• Runge-Kutta Order Conditions
• butcher

Cites Work

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• Symbolic derivation of Runge-Kutta methods
• A parameter study of explicit Runge-Kutta pairs of orders 6(5)
• Solving Ordinary Differential Equations I
• Cheap Error Estimation for Runge--Kutta Methods
• High Phase-Lag-Order Runge--Kutta and Nyström Pairs
• Runge-Kutta Pairs For Scalar Autonomous Initial Value Problems
• A New Recurrence for Computing Runge–Kutta Truncation Error Coefficients
• A General Family of Explicit Runge–Kutta Pairs of Orders $6(5)$
• Optimized explicit Runge-Kutta pair of orders \(9(8)\)

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