A family of embedded Runge-Kutta formulae
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The integration of ODE solvers, particularly adaptive step-size methods such as Dormand-Prince and Runge-Kutta schemes, facilitates numerically stable forward propagation through continuous depth.
“The integration of ODE solvers, particularly adaptive step-size methods such as Dormand-Prince and Runge-Kutta schemes, facilitates numerically stable forward propagation through continuous depth20.”
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“The integration of ODE solvers, particularly adaptive step-size methods such as Dormand-Prince and Runge-Kutta schemes, facilitates numerically stable forward propagation through continuous depth 20 .”
- Authors
- Dormand, J. R., & Prince, P. J.
- Affiliations
- Teesside University (GB)
- Venue
- Journal of Computational and Applied Mathematics
- Publisher
- Elsevier BV
- Published
- 1980-03
- Volume
- 6
- Issue
- 1
- Pages
- 19-26
- ISSN
- 0377-0427 (ISSN-L)
- OpenAlex
- W2144144709
- Cited by
- 3,634
- References
- 0
- Citations by year
- 2026: 237 · 2025: 262 · 2024: 276 · 2023: 283 · 2022: 242 · 2021: 296 · 2020: 221 · 2019: 201 · 2018: 169 · 2017: 146 · 2016: 132 · 2015: 132 · 2014: 114 · 2013: 121 · 2012: 97
- FWCI
- 0.53
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Computational and Applied Mathematics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Physical Sciences › Engineering › Computational Mechanics › Computational Fluid Dynamics and Aerodynamics
- Keywords
- absolute stability, stability region, fifth-order methods, ordinary differential equations
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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