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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Enhancements to Chebyshev-Picard Iteration Efficiency for Generally Perturbed Orbits and Constrained Dynamical Systems
TL;DR: A body of work is presented that serves to enhance the overall performance and the algorithmic automation of MCPI, applied to the problem of perturbed orbit propagation, and an M CPI framework is derived that greatly improves MCPi performance for ODE systems that intrinsically have associated conserved quantities.
Book ChapterDOI
Epidemiology of Infectious Diseases
Avner Friedman,Chiu-Yen Kao +1 more
TL;DR: Major areas of epidemiological study include disease etiology, disease break, disease surveillance, and comparison of treatment effects such as in clinical trials.
Proceedings ArticleDOI
On the Robustness to Adversarial Examples of Neural ODE Image Classifiers
TL;DR: This paper shows that Neural ODE are natively more robust to adversarial attacks with respect to state-of-the-art residual networks, and some of their intrinsic properties, such as adaptive computation cost, open new directions to further increase the robustness of deep-learned models.
Journal ArticleDOI
An adaptive step size controller for iterative implicit methods
TL;DR: In this article, a step size selection strategy that adaptively reduces the computational cost (per unit time step) as the simulation progresses, constraint by the tolerance specified, has been proposed for non-stiff ordinary differential equations and for partial differential equations where the linear systems of equations resulting from an implicit integrator are solved by direct methods.
Journal ArticleDOI
An alternative method for the integration of continuum damage evolution laws
Mathias Wallin,Matti Ristinmaa +1 more
TL;DR: In this paper, the elasto-plastic constitutive equations are reformulated using the assumption of constant strain rate direction within a load increment, which results in a significantly reduced set of ODEs, allowing an efficient integration scheme to be obtained.
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.
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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