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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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Lagrangian predictability assessed in the East China Sea

Helga S. Huntley, +2 more
- 01 Jan 2011 - 
TL;DR: In this paper, a group of 30 surface drifters, launched over a 4-day period as part of a US Navy exercise in early October 2007, are used to assess the predictability of trajectories in a confined geographic region at the northwestern edge of the Kuroshio north of Taiwan.
Journal ArticleDOI

Achieving Seventh-Order Amplitude Accuracy in Leapfrog Integrations

Paul Williams
- 28 Aug 2013 - 
TL;DR: In this paper, it was shown that leapfrog time-stepping over a suitably weighted blend of the filtered and unfiltered tendencies eliminates the third-order amplitude errors and yields fifth-order accuracy.
Journal ArticleDOI

An embedded runge–kutta method with phase-lag of order infinity for the numerical solution of the schrödinger equation

T. E. Simos
- 01 Sep 2000 - 
TL;DR: An embedded Runge-Kutta method with phase-lag of order infinity for the numerical integration of Schrodinger equation is developed in this paper, and the methods of the embedded scheme have algebraic orders five and four.
Journal ArticleDOI

Copper Retention Kinetics in Acid Soils

J.E. López-Periago, +6 more
- 01 Jan 2008 - 
TL;DR: In this article, the retention and release kinetics of Cu on four acid Typic haplumbrepts developed on two different types of parent rock material (granite and amphibolite) were studied with a stirred-fl ow chamber (SFC) method.
Journal ArticleDOI

Forward and adjoint sensitivity analysis with continuous explicit Runge-Kutta schemes

Mihai Alexe, +1 more
- 15 Feb 2009 - 
TL;DR: This work proposes to use the dense output mechanism built in the continuous Runge–Kutta schemes as a highly accurate and cost-efficient interpolation method in the inverse problem run of adaptive time integration of nonlinear models.
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.