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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.
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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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Efficient simulation of Hybrid Renewable Energy Systems

Gustavo Migoni, +5 more
- 24 Aug 2016 - 
TL;DR: A new family of numerical algorithms called Quantized State Systems (QSS) is analyzed that are more than one order of magnitude faster than the most efficient classic solvers, allowing to simulate Hybrid Renewable Energy Systems in reasonable times.
Journal ArticleDOI

Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.'s

Higinio Ramos, +1 more
- 01 Jul 2007 - 
TL;DR: The question of how to extend Chebyshev approximations for numerically solving second-order differential equations to variable stepsize procedures is the primary topic of this paper.
Journal ArticleDOI

Orbit design for future SpaceChip swarm missions in a planetary atmosphere

Camilla Colombo, +1 more
- 01 Jun 2012 - 
TL;DR: In this paper, the effect of solar radiation pressure and atmospheric drag on the orbital dynamics of satellites-on-a-chip (SpaceChips) is exploited to design equatorial long-lived orbits about the oblate Earth.
Journal ArticleDOI

Dynamic investigation of traction motor bearing in a locomotive under excitation from track random geometry irregularity

Yuqing Liu, +3 more
TL;DR: In this article, the development of railway locomotive towards high-speed and high-power has a higher requirement on traction motor bearing under the intensified wheel-rail interactions since the dynamic performance of the locomotive is increased.
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EVICAN-a balanced dataset for algorithm development in cell and nucleus segmentation

Mischa Schwendy, +3 more
- 01 Jun 2020 - 
TL;DR: A new dataset, EVICAN—Expert visual cell annotation, comprising partially annotated grayscale images of 30 different cell lines from multiple microscopes, contrast mechanisms and magnifications that is readily usable as training data for computer vision applications is presented.
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.