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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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Journal ArticleDOI

Phytotoxicity of salt and plant salt uptake: Modeling ecohydrological feedback mechanisms

Peter Bauer-Gottwein, +3 more
- 01 Apr 2008 - 
TL;DR: In this paper, a new model of phytotoxicity of salt and plant salt uptake is presented and is coupled to an existing three-dimensional groundwater simulation model, based on experimental findings from willow trees grown in hydroponic solution.
Journal ArticleDOI

Synchronous and asynchronous bursting states: role of intrinsic neural dynamics.

Takashi Takekawa, +2 more
- 27 Mar 2007 - 
TL;DR: The synchronization behavior couples tightly to the bursting mode in a wide class of networks of bursting neurons, using a mathematically tractable neuron model from the NaP current-based neuron model.
Dissertation

Analyse non-linéaire des instabilités multiples aux interfaces frottantes : application au crissement de frein

Nicolas Coudeyras
TL;DR: In this paper, a methode non-lineaire originale, based on the methodes classiques de balance harmonique, permet de calculer the reponse dynamique des systemes autonomes non-linearaires.
Journal ArticleDOI

Spectroscopy of the Young Stellar Association Price-Whelan 1: Origin in the Magellanic Leading Arm and Constraints on the Milky Way Hot Halo.

David L. Nidever, +12 more
- 11 Oct 2019 - 
TL;DR: In this paper, spectroscopic measurements of stars in the recently discovered young stellar association Price-Whelan 1 (PW 1), which was found in the vicinity of the Leading Arm (LA) of the Magellanic Stream, were reported.
Journal ArticleDOI

Highly continuous Runge-Kutta interpolants

Desmond J. Higham
- 01 Sep 1991 - 
TL;DR: It is shown that it is possible to construct terpolants with arbltrardy manycontinuous derivatives which have the same asymptotic accuracy and basic cost as the Hermite interpol ants.
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.