Parallel iteration of high-order Runge-Kutta methods with stepsize control
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Publication:1824359
DOI10.1016/0377-0427(90)90200-JzbMath0682.65039MaRDI QIDQ1824359
P. J. van der Houwen, B. P. Sommeijer
Publication date: 1990
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
stepsize controlpredictorsparallel computerfunctional iterationhigh order implicit Runge-Kutta methodnonstiff differential equations
Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)
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Cites Work
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- Unnamed Item
- High order embedded Runge-Kutta formulae
- Note on explicit parallel multistep Runge-Kutta methods
- Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
- On quadrature methods for highly oscillatory integrals and their implementation
- High-order Explicit Runge-Kutta Formulae, Their Uses, and Limitations
- Comparing Numerical Methods for Ordinary Differential Equations
- Implicit Runge-Kutta Processes
