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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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Simulation of turbulent electrocoalescence

Jens A. Melheim, +1 more
- 01 Jul 2006 - 
TL;DR: In this article, a numerical framework based on the Eulerian-Lagrangian approach is presented, where the turbulent dispersion and the inter-droplet hydrodynamic and electrical forces are carefully handled.
Journal ArticleDOI

Semi-analytical study of variable charge dust acoustic solitary waves in a dusty plasma with a q-nonextensive ion velocity distribution

Rabia Amour, +1 more
- 01 Sep 2011 - 
TL;DR: In this article, an attempt is made to study variable charge dust acoustic (DA) solitons within the theoretical framework of the Tsallis statistical mechanics and the correct nonextensive ion charging current is presented for the first time based on the orbit motion limited (OML) approach.
Journal ArticleDOI

Complex Flow Dynamics in Dense Granular Flows—Part I: Experimentation

Piroz Zamankhan, +1 more
- 01 Jul 2006 - 
TL;DR: In this article, a model was built to investigate the fluid dynamics of granular flows in an intermediate regime where both collisional and frictional interactions may affect the flow behavior, by applying a methodology useful for analysis of complex fluids based on a synergistic combination of experiments, computer simulations, and theoretical investigation.
Journal ArticleDOI

High-order parabolic beam approximation for aero-optics

Michael D. White
- 01 Aug 2010 - 
TL;DR: The parabolic beam equations are solved using high-order compact differences for the Laplacians and Runge-Kutta integration along the beam path to give a quantitative assessment of the other methods as well as being amenable to the addition of more physics.
Journal ArticleDOI

An accomplished phase FD process for DEs in chemistry

Marina A. Medvedeva, +1 more
- 01 Nov 2019 - 
TL;DR: In this paper, the evolvent of newly FD process which can be applied efficiently on the DEs in Chemistry is discussed and the FD process can be used to solve the DE problem.
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.