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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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A time-staggered partitioned coupling algorithm for transient heat conduction

P.B. Nakshatrala, +2 more
- 18 Jun 2009 - 
TL;DR: This work presents a time‐staggered partitioned coupling algorithm for transient heat conduction finite element simulations that enables arbitrary time integration schemes and meshes to be coupled with different timesteps in the various subdomains.
Journal ArticleDOI

Real-Time Switched Model Predictive Control for a Cyber-Physical Wind Turbine Emulator

Mohammed Moness, +1 more
- 01 Jun 2020 - 
TL;DR: The analysis and investigation of results highlight the feasibility and capability of SMPC for handling control objectives of WT systems within real-time using short control periods.
Proceedings ArticleDOI

Building Normalizing Flows with Stochastic Interpolants

Michael S. Albergo, +1 more
TL;DR: A simple generative model based on a continuous-time normalizing flow between any pair of base and target probability densities which allows one to map methods based on stochastic differential equations to those using ordinary differential equations, simplifying the mechanics of the model, but capturing equivalent dynamics.
Journal ArticleDOI

Dynamic modeling and motion analysis for a dual-buoyancy-driven full ocean depth glider

Shuxin Wang, +5 more
- 01 Sep 2019 - 
TL;DR: In this article, a dual-buoyancy-driven mechanism for Petrel-X, a full ocean depth glider, to adjust its buoyancy and pitch angle simultaneously is presented.
Journal ArticleDOI

Long Term Object Drift Forecast in the Ocean with Tide and Wind

Pierre Ailliot, +2 more
- 03 Aug 2006 - 
TL;DR: A new method is proposed to forecast the drift of objects in the near coastal ocean over a period of several weeks using Monte Carlo simulations to decrease the computational cost with a statistical method in order to take into account the variability of meteorological loading factors.
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.