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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Formation of disc galaxies in preheated media: a preventative feedback model
Yu Lu,Houjun Mo,Risa H. Wechsler +2 more
TL;DR: In this paper, a semi-analytic galaxy formation model implementing a self-consistent treatment for the hot halo gas configuration and the assembly of central disks is introduced, where the circum-halo medium is assumed to be preheated up to a certain entropy level by early starbursts or other processes, and compare it with an ejective feedback model, in which baryons are first accreted into dark matter halos and subsequently ejected out by feedback.
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Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE.
TL;DR: A family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations that enter the derivative symbolically and it is just-in-time-compiled, allowing the user to efficiently integrate differential equations from a higher-level interpreted language.
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Model of J_2 perturbed satellite relative motion with time-varying differential drag
TL;DR: In this article, the authors revisited the modeling of the relative motion between satellites flying in near-circular low-Earth-orbits, where the motion is described through relative orbital elements and both Earth's oblateness and differential drag perturbations are addressed.
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Impact of flow routing on catchment area calculations, slope estimates, and numerical simulations of landscape development
Eitan Shelef,George E. Hilley +1 more
TL;DR: In this paper, the authors compare commonly used flow-routing rules as well as a new routing rule to commonly used benchmarks and compare results for different routing rules using Airborne Laser Swath Mapping (ALSM) topography.
Posted Content
Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting
Vincent Le Guen,Yuan Yin,Jérémie Dona,Ibrahim Ayed,Emmanuel de Bézenac,Nicolas Thome,Patrick Gallinari +6 more
TL;DR: The APHYNITY framework is introduced, a principled approach for augmenting incomplete physical dynamics described by differential equations with deep data-driven models and can efficiently leverage approximate physical models to accurately forecast the evolution of the system and correctly identify relevant physical parameters.
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.
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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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