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Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control
TLDR
Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.Abstract:
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Journal ArticleDOI
A family of embedded Runge-Kutta formulae
J. R. Dormand,P.J. Prince +1 more
TL;DR: 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.
Book ChapterDOI
Numerical Solution of Ordinary Differential Equations
TL;DR: Several numerical methods for solving systems of ordinary differential equations are presented in this paper, including multistep methods and single step methods, with particular emphasis on the application of these methods to problems in dynamical astronomy.
Journal ArticleDOI
High order embedded Runge-Kutta formulae
P.J. Prince,J. R. Dormand +1 more
TL;DR: In this article, the criteria to be satisfied by embedded Runge-Kutta pairs of formulae are reviewed, together with tests on their efficiency relative to other high-order forms in current use.
Journal ArticleDOI
New features of the software MatCont for bifurcation analysis of dynamical systems
TL;DR: Software issues that are in practice important for many users, e.g. how to define a new system starting from an existing one, how to import and export data, system descriptions, and computed results are discussed.
Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
TL;DR: These new formulas are suitable for the numerical integration of heat transfer problems after discretisation of these problems in the space variables, since stability considerations, occurring in such problems, would eliminate the benefits of high-orderRunge-Kutta formulas.