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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.
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.

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Citations
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Predictions of aneurysm formation in distensible tubes: Part A—Theoretical background to alternative approaches

Andrea Bucchi, +1 more
- 01 Jun 2013 - 
TL;DR: In this article, the authors investigated aneurysm development using both non-linear finite element analyses and distinct alternative formulations and solution techniques and found that inconsistencies were observed between the material properties used in a nonlinear finite-element analysis and the material characteristics of the specimen used to provide experimental measurements for comparison.
Journal ArticleDOI

Fragility functions and behavior factors estimation of multi-story cross-laminated timber structures characterized by an energy-dependent hysteretic model:

Angelo Aloisio, +2 more
- 01 Feb 2021 - 
TL;DR: In this paper, the fragility functions and behavior factors of cross-laminated timber (CLT) structures were assessed and the structures derived from the assembly of single CLT wall panels characterized by diff...
Journal ArticleDOI

The unscented kalman filter, a powerful tool for data analysis

A. Sitz, +2 more
- 01 Jun 2004 - 
TL;DR: A derivation of the unscented Kalman filter as an approximation to the optimal Bayesian filter equations is presented and the potentials of the UKF are demonstrated for the problem of simultaneous estimation of states and parameters from noise corrupted data of nonlinear dynamical systems.
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Numerical robustness of extended Kalman filtering based state estimation in ill‐conditioned continuous‐discrete nonlinear stochastic chemical systems

G. Yu. Kulikov, +1 more
- 25 Mar 2019 - 
Journal ArticleDOI

Projection methods preserving Lyapunov functions

Manuel Calvo, +3 more
- 05 Mar 2010 - 
TL;DR: This approach extends previous work of Grimm and Quispel, allowing the use of Runge–Kutta methods for which the associated quadrature formula does not need to have positive or zero coefficients.
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.