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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.
About: 
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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Three months of COVID-19: A systematic review and meta-analysis.

Danish Rafiq, +2 more
- 01 Jul 2020 - 
TL;DR: Some recently proposed conceptual models that estimate the spread of this disease based on the basic reproductive number for better prevention and control procedures are shed light on how the virus has endangered the global economy.
Journal ArticleDOI

Thermofield Theory for Finite-Temperature Coupled Cluster.

Gaurav Harsha, +2 more
- 19 Sep 2019 - 
TL;DR: A coupled cluster and linear response theory is presented to compute properties of many-electron systems at non-zero temperatures by parameterizing the so-called thermal state using an exponential ansatz with cluster operators that create thermal quasiparticle excitations on a mean-field reference.
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Associating quantitative behavioral traits with gene expression in the brain

Anat Reiner-Benaim, +6 more
- 15 Aug 2007 - 
TL;DR: The hierarchical FDR testing strategies presented here can serve beyond the structure of the motivating example study to any complex microarray study, and are suitable for screening by testing related hypotheses, then testing the hypotheses of interest.
Journal ArticleDOI

A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

Amir Mehdi Dehrouyeh-Semnani, +3 more
- 01 Oct 2016 - 
TL;DR: In this article, a mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale, which is based on the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles.
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Implementation algorithm for a single hardening constitutive model for frictional materials

K. P. Jakobsen, +1 more
- 01 Jun 2002 - 
TL;DR: In this article, an advanced elasto-plastic constitutive model for frictional materials, whose incremental version is presented in a companion paper (Int. Numer. Meth. Anal. Geomech., 2002; 26:647), is implemented in a user defined material module.
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.