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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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Long-Term Rotational Motion Analysis and Comparison to Observations of the Inoperative Envisat

Luc Sagnières, +1 more
- 01 Feb 2019 - 
TL;DR: In this paper, a new model for the analysis and prediction of the rotational motion of large space debris over a long term is presented, and a formulation for a high-order gravity-gradient torque is derived.
Journal ArticleDOI

A family of three-stage third order AMF-W-methods for the time integration of advection diffusion reaction PDEs.

Severiano González-Pinto, +3 more
- 01 Feb 2016 - 
TL;DR: New three-stage W-methods for the time integration of semi-discretized advection diffusion reaction Partial Differential Equations are provided and numerical illustration on practical PDE problems revealing that the new methods are good competitors over existing integrators in the literature.
Journal ArticleDOI

Impact of wall discretization on the modeling of heating/cooling energy consumption of residential buildings

Mattia De Rosa, +3 more
- 01 Jan 2016 - 
TL;DR: In this article, the authors investigated the simulation of the thermal performance of a benchmark residential building using a self-developed dynamic code implemented in the dedicated software called Building Energy Performance Simulator (BEPS), validated in a previous authors' work.
Journal ArticleDOI

A study of the avalanche-to-streamer transition in arbitrary gases by particle simulation

Mohamed Rabie, +1 more
- 29 Mar 2016 - 
TL;DR: In this article, the authors systematically investigate the avalanche-to-streamer transition (AST) over a wide range of pressures and homogenous background electric fields and for a comprehensive list of gases, namely pure nitrogen, carbon dioxide, oxygen, argon, sulfur hexafluoride and synthetic air.
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Dynamic modeling of a H2O-permselective membrane reactor to enhance methanol synthesis from syngas considering catalyst deactivation

Mohammad Farsi, +1 more
- 01 Jul 2012 - 
TL;DR: In this paper, the effect of water vapor removal on methanol synthesis capacity from syngas in a fixed-bed membrane reactor is studied considering long-term catalyst deactivation.
References
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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.