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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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Citations
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High-performance high-order simulation of wave and plasma phenomena

Jan S. Hesthaven, +1 more
TL;DR: This thesis presents results aiming to enhance and broaden the applicability of the discontinuous Galerkin (DG) method in a variety of ways and introduces new explicit multi-rate time integrators for ordinary differential equations with multiple time scales, with a focus on applicability to DG discretizations of time-dependent problems.
Journal ArticleDOI

Lead-Lag Damper Robustness Analysis for Helicopter Ground Resonance

Giuseppe Quaranta, +2 more
- 02 Jul 2013 - 
TL;DR: In this article, the robustness of the ground resonance problem is analyzed in a form that isolates a closed loop containing the lead-lag damper, which is considered the uncertain component.
Posted Content

Minimal model of cellular symmetry breaking

Alexander Mietke, +4 more
- 26 Sep 2019 - 
TL;DR: It is shown that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities.
Posted Content

Adversarial Robustness of Stabilized NeuralODEs Might be from Obfuscated Gradients.

Yifei Huang, +4 more
- 28 Sep 2020 - 
TL;DR: A provably stable architecture for Neural Ordinary Differential Equations (ODEs) which achieves non-trivial adversarial robustness under white-box adversarial attacks even when the network is trained naturally, and Inspired by dynamical system theory, a stabilized neural ODE network named SONet whose ODE blocks are skew-symmetric and proved to be input-output stable.
Journal ArticleDOI

Parameter estimation of the FitzHugh-Nagumo model using noisy measurements for membrane potential

Yanqiu Che, +4 more
- 14 Jun 2012 - 
TL;DR: This paper proposes an identification method to estimate the parameters of the FitzHugh-Nagumo (FHN) model for a neuron using noisy measurements available from a voltage-clamp experiment, and demonstrates the effectiveness of the proposed method.
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.