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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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Journal ArticleDOI

Effective vaccine allocation strategies, balancing economy with infection control against COVID-19 in Japan.

Satoshi Sunohara, +6 more
- 02 Sep 2021 - 
TL;DR: In this paper, the authors evaluated various vaccine and intensive countermeasure strategies with constraint of economic loss using SEIR model to obtain knowledge of how to balance economy with infection control in Japan.
Dissertation

Drag reduction by passive in-plane wall motions in turbulent wall-bounded flows

Tamás I. Józsa
TL;DR: In this paper, Choi et al. explored the hypothesis that passive wall motions driven by fluid mechanical forces are able to reduce the friction drag in fully developed turbulent boundary layers, and two theoretical passive compliant wall models are proposed, the aim being to sustain beneficial wall motions identified by active flow control simulations.
Journal ArticleDOI

Runge–Kutta pairs suited for SIR‐type epidemic models

Vladislav N. Kovalnogov, +4 more
- 01 Apr 2021 - 
TL;DR: In this article, a new Runge-Kutta (RK) pair of orders five and four was constructed for this type of ODEs and its superiority over standard RK pairs from the literature is illustrated when applied to various epidemic models.
Journal ArticleDOI

Dynamical pruning of the non-equilibrium quantum dynamics of trapped ultracold bosons

F. Köhler, +4 more
- 05 Aug 2019 - 
TL;DR: In this paper, a dynamical pruning approach in the framework of the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) is presented to tackle the issue of nonequilibrium quantum dynamics of bosonic many-body systems.
Journal ArticleDOI

Constraining the equation of state in modified gravity via universal relations

V. I. Danchev, +1 more
- 25 Jan 2021 - 
TL;DR: In this paper, the authors generalize these relations to scalarized neutron stars in massive scalar-tensor theories and prove that the resulting relations for scalarised neutron stars are indeed EOS independent up to a large extent and they can be significantly different compared to General Relativity.
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.