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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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Heliocentric Solar Sail Orbit Transfers with Locally Optimal Control Laws

Malcolm Macdonald, +2 more
- 01 Jan 2007 - 
TL;DR: In this article, the authors proposed a trajectory generation method for a solar sailing mission with the absence of reaction mass from the primary propulsion system, such as a Solar Polar Orbiter or an Interstellar Heliopause Probe.
Journal ArticleDOI

Polar rotation angle identifies elliptic islands in unsteady dynamical systems

Mohammad Farazmand, +1 more
- 01 Feb 2016 - 
TL;DR: In this article, the polar decomposition of the flow gradient is used as a diagnostic for elliptic invariant regions in non-autonomous dynamical systems, where the authors consider two-dimensional systems and derive explicit formulas using the singular values and vectors of flow gradient.
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Comparison of Selected Methods of Handling Redundant Constraints in Multibody Systems Simulations

Marek Wojtyra, +1 more
- 01 Apr 2013 - 
Journal ArticleDOI

Predicting the hypervelocity star population in Gaia

T. Marchetti, +5 more
- 01 Jun 2018 - 
TL;DR: In this article, the authors present the expected sample size and properties (mass, magnitude, spatial, velocity distributions) of hypervelocity stars (HVSs) in the Gaia stellar catalogue.
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Strictures of a microchannel impose fierce competition to select for highly motile sperm

Meisam Zaferani, +2 more
- 01 Feb 2019 - 
TL;DR: Motility-based competition dynamics at microfluidic strictures suggests a sperm-selection mechanism in the reproductive tract and investigates sperm locomotion in the presence of external fluid flow and geometries simulating the female reproductive tract to lead to a better understanding of sperm motion during fertilization.
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.