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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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Accurate and approximate integrations of Drucker–Prager plasticity with linear isotropic and kinematic hardening

Mohammad Rezaiee-Pajand, +2 more
- 01 May 2011 - 
TL;DR: In this article, two explicit approximate integration schemes based on exponential maps, for non-hardening material obeying Drucker-Prager's criterion, have been presented, and the accuracies of the suggested approximate algorithms are assessed by creating related iso-error maps.
Journal ArticleDOI

Embedded diagonally implicit Runge-Kutta-Nystrom 4(3) pair for solving special second-order IVPs

Raed Ali Al-Khasawneh, +2 more
- 15 Jul 2007 - 
TL;DR: Third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed, which has the property of minimized local truncation error and the last row of the coefficient matrix is equal to the vector output.
Journal ArticleDOI

Finite-size Lagrangian coherent structures in thermocapillary liquid bridges

Francesco Romanò, +1 more
TL;DR: In this paper, a numerical investigation showed that finite-size Lagrangian coherent structures result from bulk transport near Kolmogorov-Arnold-Moser tori and a dissipative effect near the free surface.
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Targeted Energy Transfer Between a Swept Wing and Winglet-Housed Nonlinear Energy Sink

Sean A. Hubbard, +4 more
- 01 Dec 2014 - 
TL;DR: In this article, a prototype nonlinear energy sink, whose design is based upon parameters determined to effectively suppress transonic aeroelastic instabilities of a wind-tunnel wing model via passive targeted energy transfer, is introduced.
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Nearshore sandbar rotation at single-barred embayed beaches

Brice Blossier, +3 more
- 01 Apr 2016 - 
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.