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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Disease Localization in Multilayer Networks
Guilherme Ferraz de Arruda,Guilherme Ferraz de Arruda,Emanuele Cozzo,Tiago P. Peixoto,Tiago P. Peixoto,Francisco A. Rodrigues,Yamir Moreno,Yamir Moreno +7 more
TL;DR: In this paper, a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation was presented, extending the models of monoplex networks to this context, and analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible-infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario were derived.
Journal ArticleDOI
A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation
Fei Hui,T. E. Simos,T. E. Simos +2 more
TL;DR: In this article, a family of two stage low computational cost symmetric two-step methods with vanished phase-lag and its derivatives is developed, and the local truncation error, the interval of periodicity and the effect of the vanishing of the phaselag and their derivatives on the efficiency of the obtained method are also studied.
Journal ArticleDOI
The secondary Bjerknes force between two gas bubbles under dual-frequency acoustic excitation
Yuning Zhang,Shengcai Li +1 more
TL;DR: The secondary Bjerknes force under dual-frequency excitation is investigated both analytically and numerically within a large parameter zone, revealing the unique characteristics of the parameter zone for sign change and the combination resonances.
Journal ArticleDOI
A reconsideration of some embedded Runge-Kutta formulae
J. R. Dormand,P J Prince +1 more
TL;DR: The RK5(4) and RK6(5) embedded Runge-Kutta formulae are reconsidered with regard to enlarging regions of absolute stability while retaining satisfactory truncation error norms as mentioned in this paper.
Posted Content
Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
TL;DR: This work provides a theoretical sufficient criterion showing that the distribution generated by equivariant normalizing flows is invariant with respect to these symmetries by design, and proposes building blocks for flows which preserve symmetry which are usually found in physical/chemical many-body particle systems.
References
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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.
Journal ArticleDOI
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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