A family of embedded Runge-Kutta formulae
J. R. Dormand,P.J. Prince +1 more
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.read more
Citations
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Development of a new superfluid helium ultra-cold neutron source and a new magnetic trap for neutron lifetime measurements
TL;DR: In this paper, the development of an ultra-cold neutron (UCN) source at the Institut Laue-Langevin (ILL) based on super-thermal down-scattering of a cold neutron beam in superfluid helium is described.
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An efficient axial-flexure-shear fiber beam model for dynamic analyses of beam–column framed structural systems under impact loading
Fang Yi Zhou,Jijia Zhong +1 more
TL;DR: In this article , the authors developed a more general-purpose simplified impact model for dynamic analyses of beam-column framed structural systems under impact loading with consideration of shear effects in beamcolumn members.
On Eight-Step Methods with Vanished Phase-Lag and Its Derivatives for the Numerical Solution of the Schrodinger Equation
Ibraheem Alolyan,T. E. Simos +1 more
TL;DR: In this article, the authors developed new algebraic order eight-step methods with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical integration of the radial.
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Gas phase methanol synthesis with Raman spectroscopy for gas composition monitoring
TL;DR: In this article, the applicability of Raman spectroscopy for time-resolved gas composition monitoring during direct methanol synthesis via carbon dioxide hydrogenation was investigated, and a data reconciliation algorithm was developed to estimate the occurring chemical reactions' extents by iterative minimization of the difference between concentration values acquired from the experimental data and concentration values computed based on the mass conservation principle.
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On the modelling of the shear thickening behavior in micellar solutions
Gabriel Landázuri,E. R. Macías,Juan Paulo García-Sandoval,Elena Hernández,Octavio Manero,Jorge E. Puig,F. Bautista +6 more
TL;DR: In this paper, the steady and transient nonlinear rheological behaviors of dilute rod-like micellar solutions are predicted with a particular case of the generalized Bautista-Manero-Puig (BMP) model that consists of the upper-convected Maxwell constitutive equation and a dissipative power-dependent kinetic equation, which takes into account the formation and disruption of shear-induced structures (SISs).
References
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Journal ArticleDOI
Comparing Numerical Methods for Ordinary Differential Equations
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.
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Coefficients for the study of Runge-Kutta integration processes
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
TL;DR: Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.
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