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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Inner-shell multiple ionization of polyatomic molecules with an intense x-ray free-electron laser studied by coincident ion momentum imaging
Benjamin Erk,Daniel Rolles,Lutz Foucar,Benedikt Rudek,Sascha W. Epp,Max J. Cryle,Christoph Bostedt,Sebastian Schorb,Sebastian Schorb,John D. Bozek,Arnaud Rouzée,Axel Hundertmark,Tatiana Marchenko,Marc Simon,Frank Filsinger,Lauge Christensen,Sankar De,Sankar De,Sebastian Trippel,Jochen Küpper,Henrik Stapelfeldt,Shin-ichi Wada,Shin-ichi Wada,Kiyoshi Ueda,Michele Swiggers,Marc Messerschmidt,Claus Dieter Schröter,Robert Moshammer,Ilme Schlichting,Joachim Ullrich,Joachim Ullrich,Artem Rudenko,Artem Rudenko +32 more
TL;DR: In this article, the ionization and fragmentation of two selenium containing hydrocarbon molecules, methylselenol (CH3SeH) and ethylselenolate (C2H5SeH), by intense (>1017 W cm−2) 5 fs x-ray pulses with photon energies of 1.7 and 2.
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Visibility graphlet approach to chaotic time series
TL;DR: The results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.
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Optimized explicit Runge-Kutta pair of orders 9(8)
TL;DR: A fully explicit algorithm for deriving a Runge–Kutta pair of orders 9(8) is presented and an optimal pair is given, which is found to outperform all other published Runge-KutTA pairs when severe tolerances are required.
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Minimal Model of Cellular Symmetry Breaking
TL;DR: In this article, a model of the self-organization of the cell cortex is presented based on a hydrodynamic theory of curved active surfaces, where active stresses on this surface are regulated by diffusing molecular species.
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An embedded phase-fitted modified Runge–Kutta method for the numerical integration of the radial Schrödinger equation
TL;DR: Applications of the new couple to several problems arising from the radial Schrodinger equation indicate that the new pair is more efficient than other well known comparable embedded Runge–Kutta pairs.
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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