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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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Posted Content

How to train your neural ODE: the world of Jacobian and kinetic regularization

Chris Finlay, +3 more
- 07 Feb 2020 - 
TL;DR: This paper introduces a theoretically-grounded combination of both optimal transport and stability regularizations which encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well, leading to faster convergence and to fewer discretizations of the solver.
Journal ArticleDOI

Metabolism of complement factor D in renal failure.

Manuel Pascual, +5 more
- 01 Oct 1988 - 
TL;DR: Factor D synthesis was not significantly altered by renal function, and did not correlate with C-reactive protein, suggesting that factor D is not an acute phase protein.
Book ChapterDOI

From petri nets to differential equations – an integrative approach for biochemical network analysis

David Gilbert, +1 more
TL;DR: It is shown that analysis based on a discrete Petri net model of the system can be used to derive the sets of initial concentrations required by the corresponding continuous ordinary differential equation model, and no other initial concentrations produce meaningful steady states.
Journal ArticleDOI

A Modified Phase-Fitted Runge–Kutta Method for the Numerical Solution of the Schrödinger Equation

T. E. Simos, +1 more
- 01 Jul 2001 - 
TL;DR: A modified phase-fitted Runge-Kutta method for the numerical solution of periodic initial value problems is constructed in this article, which is based on the runge-kutta fifth algebraic order method of Dormand and Prince.
Journal ArticleDOI

Exponentially fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation and related problems

T. E. Simos
- 01 Sep 2000 - 
TL;DR: Numerical and theoretical results obtained for several well-known problems show the efficiency of the new Runge–Kutta methods for the numerical integration of the radial Schrodinger equation or systems of equations.
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.