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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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Construction and validation of a rigorous surface hopping algorithm for conical crossings

Caroline Lasser, +2 more
- 01 Dec 2007 - 
TL;DR: In this article, a surface hopping algorithm for time-dependent two-level Schrodinger systems with conically intersecting eigenvalues is presented and evaluated for two-dimensional isotropic systems, which include linear Jahn-Teller Hamiltonians and Gaussian initial data.
Journal ArticleDOI

Evaluation of models for supercritical fluid extraction

Amit Rai, +3 more
- 01 May 2014 - 
TL;DR: In this paper, two models for the modeling of supercritical extraction process are studied and validated using published experimental data, one model considers internal mass transfer coefficient as the controlling parameter for the extraction process, and the second model analyzes the dynamic behavior of the extractive process by considering intra-particle diffusion and external mass transfer.
Posted Content

How to train your neural ODE

Chris Finlay, +3 more
- 07 Feb 2020 - 
TL;DR: In this paper, a theoretically-grounded combination of both optimal transport and stability regularization is proposed to encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well.
Journal ArticleDOI

Developing a delay differential equation solver

Christopher A. H. Paul
- 01 Apr 1992 - 
TL;DR: In this paper, the authors discuss various properties to be tested when designing a robust code for delay differential equations: choice of interpolant; tracking of discontinuities; vanishing delays; and problems arising from floating point arithmetic.
Journal ArticleDOI

A dispersive-fitted and dissipative-fitted explicit Runge–Kutta method for the numerical solution of orbital problems

Zacharias Anastassi, +1 more
- 01 Nov 2004 - 
TL;DR: In this paper, a new explicit Runge-Kutta method with minimum error of the fifth algebraic order and infinite order of dispersion and dissipation has been presented.
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.