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Open AccessJournal ArticleDOI

A family of embedded Runge-Kutta formulae

J. R. Dormand, +1 more
- 01 Mar 1980 - 
- Vol. 6, Iss: 1, pp 19-26
TLDR
In this article, a family of embedded Runge-Kutta formulae RK5 (4) are derived from these and a small principal truncation term in the fifth order and extended regions of absolute stability.
About: 
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1980-03-01 and is currently open access. It has received 3106 citations till now.

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Citations
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Proceedings ArticleDOI

Exploiting perception in high-fidelity virtual environments (Additional presentations from the 24th course are available on the citation page)

Mashhuda Glencross, +4 more
TL;DR: The principles of human perception guide important development of algorithms and techniques in collaboration, graphical, auditory, and haptic rendering, and it is shown how human perception is exploited to achieve realism in high fidelity environments within the constraints of available finite computational resources.
Journal ArticleDOI

A benchmark test of accuracy and precision in estimating dynamical systems characteristics from a time series.

Sietse M. Rispens, +7 more
- 22 Jan 2014 - 
TL;DR: A set of standardized time series with well-defined dynamical characteristics that serve as a benchmark test and can be used to evaluate and tune any estimation method to perform optimally for arbitrary experimental data is presented.
Journal ArticleDOI

Near-infrared polarization images of the Orion proplyds

Steffen Rost, +3 more
- 01 Jul 2008 - 
TL;DR: In this paper, the authors performed AO-assisted high-resolution imaging polarimetry on selected Orion proplyds close to the Trapezium stars in the J, H, and K bands in the active Orion H II-region.
Journal ArticleDOI

Universally bistable shells with nonzero Gaussian curvature for two-way transition waves.

Nikolaos Vasios, +3 more
- 29 Jan 2021 - 
TL;DR: In this paper, a strategy to realize bistable doubly curved shells with arbitrary thickness and how to optimize the dynamic response of one-dimensional connected arrays of such shells are presented.
Journal ArticleDOI

Cooperative Orbital Control of Multiple Satellites via Consensus

Hao Zhang, +1 more
- 19 Feb 2018 - 
TL;DR: This paper assumes that the communication in the networked satellite system is represented as an undirected graph, and then implements the governing system dynamics in a control-affine form as described by the Gauss's variational equations.
References
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Book

Computational Methods in Ordinary Differential Equations

John Denholm Lambert
Journal ArticleDOI

Comparing Numerical Methods for Ordinary Differential Equations

T. E. Hull, +3 more
- 01 Dec 1972 - 
TL;DR: According to criteria involving the number of function evaluations, overhead cost, and reliability, the best general-purpose method, if function evaluations are not very costly, is one due to Bulirsch and Stoer, however, when function evaluated methods are relatively expensive, variable-order methods based on Adams formulas are best.

Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems

E. Fehlberg
Journal ArticleDOI

Coefficients for the study of Runge-Kutta integration processes

John C. Butcher
- 01 May 1963 - 
TL;DR: In this paper, a set of η first order simultaneous differential equations in the dependent variables y 1, y 2, y 3, y 4, y 5, y 6 and the independent variable x is considered.

Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control

E. Fehlberg
TL;DR: Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.