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
More filters
Journal ArticleDOI
Kassiopeia: a modern, extensible C++ particle tracking package
D. Furse,S. Groh,N. Trost,M. Babutzka,John E. Barrett,J. Behrens,N. Buzinsky,T.J. Corona,T.J. Corona,Sanshiro Enomoto,M. Erhard,Joseph A. Formaggio,Ferenc Glück,F. Harms,F. Heizmann,D. Hilk,W. Käfer,M. Kleesiek,B. Leiber,S. Mertens,N. S. Oblath,P. Renschler,J. Schwarz,P. L. Slocum,N. Wandkowsky,K. Wierman,K. Wierman,M. Zacher +27 more
TL;DR: Kassiopeia as discussed by the authors is an object-oriented software package using modern C++ techniques, written originally to meet the needs of the Katrin collaboration, which is capable of simulating particle trajectories governed by arbitrarily complex differential equations of motion.
Journal ArticleDOI
Integration of tresca and mohr-coulomb constitutive relations in plane strain elastoplasticity
Scott W. Sloan,J. R. Booker +1 more
TL;DR: In this article, the authors considered the problem of integrating the constitutive relations for Tresca and Mohr-Coulomb materials under conditions of plane strain and derived a semi-analytic method for integrating both types of constitutive law which assumes that the quantities d&/dl are constant.
Journal ArticleDOI
Insulin-regulated Glut4 Translocation MEMBRANE PROTEIN TRAFFICKING WITH SIX DISTINCTIVE STEPS
Paul Duffield Brewer,Estifanos N. Habtemichael,Irina Romenskaia,Cynthia Corley Mastick,Adelle C.F. Coster +4 more
TL;DR: Surprisingly, AS160 knockdown accelerated LRP1 exocytosis in basal and insulin-stimulated adipocytes indicates that AS160 may regulate trafficking into as well as release from GSVs, which is highly regulated through an AS160-independent process.
Journal ArticleDOI
A dynamic model of a 100 kW micro gas turbine fuelled with natural gas and hydrogen blends and its application in a hybrid energy grid
TL;DR: In this paper, the authors developed a dynamic model of a commercial 100kW micro gas turbine (MGT) fuelled with mixtures of standard (i.e. natural gas or methane) and alternative fuels (e.g. hydrogen).
Journal ArticleDOI
On nonlinear vibrations of micropipes conveying fluid
TL;DR: In this paper, the size-dependent primary resonant characteristics of a simply supported micropipe conveying fluid in subcritical domain are examined via depicting frequency-response and force-response curves.
References
More filters
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.
Related Papers (5)
Symmetric Multistep Methods for the Numerical Integration of Planetary Orbits
Gerald D. Quinlan,Scott Tremaine +1 more