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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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Model-supported optimization of phototrophic growth in a stirred-tank photobioreactor

Ezequiel Franco-Lara, +3 more
- 20 Dec 2006 - 
TL;DR: A fuzzy‐logic light attenuation model was developed and validated for a stirred‐tank photobioreactor and local light intensities were used to calculate local specific growth rates of the cyanobacteria Synechococcus PCC 7942.
Journal ArticleDOI

Global error versus tolerance for explicit Runge-Kutta methods

Desmond J. Higham
- 01 Oct 1991 - 
TL;DR: The potential for 'tolerance proportionality' in existing explicit Runge-Kutta algorithms is examined, taking account of recent developments in the derivation of high-order formulae, defect control strategies, and interpolants for continuous solution and first derivative approximations.
Journal ArticleDOI

Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8

P. W. Sharp
- 01 Sep 1991 - 
TL;DR: Numerical testing of six explicit Runge-Kutta pairs showed how the performance could be alterednoticeably by making simple changes to the stepsize selection strategy, and new ways of presenting numericalcomparisons were demonstrated.
Journal ArticleDOI

Thermal pre- and post-snap-through buckling of a geometrically imperfect doubly-clamped microbeam made of temperature-dependent functionally graded materials

Amir Mehdi Dehrouyeh-Semnani, +3 more
- 15 Jun 2017 - 
TL;DR: In this paper, a geometrically nonlinear size-dependent governing equation of a thermally loaded doubly-clamped microbeam made of temperature-dependent FGMs is derived in the framework of modified couple stress theory in conjunction with Euler-Bernoulli beam theory and the classical rule of mixture.
Journal ArticleDOI

Nonlinear Variable Structure Filter for the Online Trajectory Scaling

O. Gerelli, +1 more
- 07 Apr 2009 - 
TL;DR: A new discrete-time filter, with novel capabilities, is designed, where not only torque constraints are considered but also kinematic constraints are easily handled and the new filter always attempts to recover any delay caused by the constraints.
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.