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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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Nonclassical Responses of Oscillators with Hysteresis

Walter Lacarbonara, +1 more
- 01 May 2003 - 
TL;DR: In this paper, a path-following algorithm based on pseudo-arclength parameterization is proposed for Masing-type and Bouc-Wen hysteretic oscillators, where the pertinent state space is formulated for each system and the periodic orbits are sought as the fixed points of an appropriate Poincare map.
Journal ArticleDOI

Filament-based smoke with vortex shedding and variational reconnection

Steffen Weißmann, +1 more
TL;DR: In this article, the authors present a complete model that includes moving obstacles with vortex shedding, all represented as filaments, and the long-time behavior of their method is excellent: energy and momentum stay constant within reasonable bounds and computational complexity does not increase over time.
Journal ArticleDOI

A Runge–Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation

Kenan Mu, +2 more
- 01 Mar 2015 - 
TL;DR: In this paper, a Runge-Kutta type eight algebraic order two-step method with phase-lag and its first, second, third and fourth derivatives equal to zero is presented.
Journal ArticleDOI

Continuum modelling and simulation of granular flows through their many phases

Sachith Dunatunga, +1 more
- 01 Sep 2015 - 
TL;DR: In this paper, a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process is proposed and numerically implemented. But the model is not suitable for large deformations.
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Variability in kinematic coupling assessed by vector coding and continuous relative phase

Ross H. Miller, +4 more
- 17 Sep 2010 - 
TL;DR: The results suggest that comparisons between the findings of studies that have quantified variability using CRP and those that have used vector coding should be made with caution.
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.