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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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Citations
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A finite element model and electronic analogue of pipeline pressure transients with frequency-dependent friction

Jian-Jun Shu
- 09 Mar 2014 - 
TL;DR: A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed in this article, where basic equations are approximated to be a set of ordinary differential equations that can be represented in state space form.
Journal ArticleDOI

Wobbling double sine-Gordon kinks

João G. F. Campos, +1 more
- 01 Sep 2021 - 
TL;DR: In this article, the collision of a kink and an antikink in the double sine-Gordon model with and without the excited vibrational mode was studied, and it was shown that there is a limited range of the parameters where the resonance windows exist.
Journal ArticleDOI

Parallel Computation of Trajectories Using Graphics Processing Units and Interpolated Gravity Models

Nitin Arora, +2 more
- 08 Jun 2015 - 
TL;DR: A solution methodology is presented that takes advantage of 1) new high-fidelity geopotential and third-body perturbation models that efficiently trade memory for speed, and 2) a graphics processing unit based integrator to achieve parallelism across multiple objects.
Journal ArticleDOI

Gamma rhythmic bursts: coherence control in networks of cortical pyramidal neurons

Toshio Aoyagi, +2 more
- 01 May 2003 - 
TL;DR: In this paper, a model of chattering neurons was used to study how gamma-frequency bursting is synchronized in a network of these neurons, and it was shown that an incremental change of the bursting mode, such as from singlet to doublet, always accompanies a rapid transition from antisynchronous to synchronous firing.
Journal ArticleDOI

Modeling steady-state heterogeneous gas–solid reactors using feedforward neural networks

Daniel R. Parisi, +1 more
- 15 Sep 2001 - 
TL;DR: In this paper, a new method for solving gas-solid heterogeneous reactors is proposed, where the mass balance inside the pellet is replaced by an analytical function, which functionality corresponds to an adequate trained three-layer feedforward neural network.
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.