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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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Performance Assessment and Translation of Physiologically Based Pharmacokinetic Models From acslX to Berkeley Madonna, MATLAB, and R Language: Oxytetracycline and Gold Nanoparticles As Case Examples.

Zhoumeng Lin, +8 more
- 01 Jul 2017 - 
TL;DR: This tutorial helps beginners learn PBPK modeling, provides suggestions for selecting a suitable tool for future projects, and may lead to the transition from acslX to alternative modeling tools.
Journal ArticleDOI

The Natural 3D Spiral

Gur Harary, +1 more
- 01 Apr 2011 - 
TL;DR: This paper presents a novel mathematical definition of a 3D logarithmic spiral, which provides a proper description of objects found in nature and proves that the spiral satisfies several desirable properties, including invariance to similarity transformations, smoothness, symmetry, extensibility, and roundness.
Proceedings Article

Riemannian Score-Based Generative Modeling

Valentin De Bortoli, +5 more
TL;DR: RSGMs are introduced, a class of generative models extending SGMs to compact Riemannian manifolds and demonstrating their approach on a variety of manifolds, and in particular with earth and climate science spherical data.
Journal ArticleDOI

Embedded Runge–Kutta scheme for step-size control in the interaction picture method

Stéphane Balac, +3 more
- 01 Apr 2013 - 
TL;DR: An embedded Runge–Kutta scheme with orders 3 and 4 is presented with the aim to deliver an estimation of the local error for adaptive step-size control purposes in the Interaction Picture method and provides a local error estimate at no significant extra cost.
Journal ArticleDOI

High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

Ibraheem Alolyan, +2 more
- 23 Jul 2010 - 
TL;DR: In this paper, a high algebraic order multistep method is developed for the approximate solution of the radial Schrodinger equation, which is applied for error analysis and numerical applications.
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.