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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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Citations
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A non-gradient based algorithm for the determination of surface tension from a pendant drop: Application to low Bond number drop shapes

Nicolas J. Alvarez, +2 more
TL;DR: This study shows that this algorithm allows for surface tension measurements corresponding to Bond numbers previously shown to be ill suited for pendant drop measurements.
Journal ArticleDOI

GPU Acceleration of Runge-Kutta Integrators

Lawrence M. Murray
- 01 Jan 2012 - 
TL;DR: This work considers the use of commodity graphics processing units (GPUs) for the common task of numerically integrating ordinary differential equations (ODEs), achieving speedups of up to 115-fold over comparable serial CPU implementations, and 15-foldover multithreaded CPU code with SIMD intrinsics.
Journal ArticleDOI

Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches.

Michael J. Plank, +1 more
- 07 Nov 2012 - 
TL;DR: A new lattice-free individual-based model that incorporates cell-to-cell crowding effects and the confluent cell density is not predefined, but an emergent model property, which means that the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent latticed model.
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The PEPA eclipse plugin

Mirco Tribastone, +2 more
TL;DR: The PEPA Eclipse Plug-in supports the creation and analysis of performance models, from small-scale Markov models to large-scale simulation studies and differential equation systems.
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Slip MHD liquid flow and heat transfer over non-linear permeable stretching surface with chemical reaction

M. H. Yazdi, +3 more
- 01 Jul 2011 - 
TL;DR: In this paper, the magnetohydrodynamic (MHD) liquid flow and heat transfer over non-linear permeable stretching surface has been presented in the presence of chemical reactions and partial slip.
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.