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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Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches
TL;DR: In this article, an analytical and numerical investigation into the dynamic interaction between a cantilever beam with nonlinear damping and stiffness behavior, modeled by the Duffing-Rayleigh equation, and a non-ideal motor that is connected to the end of the beam, is presented.
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An investigation on performance and combustion characteristics of pure n-butanol and a blend of n-butanol/ethanol as fuels in a spark ignition engine
TL;DR: In this paper, the n-butanol, an alcohol with chemical characteristics similar to gasoline, was evaluated experimentally in a spark ignition (SI) engine and through two-zone computer modelling.
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Half-explicit Runge-Kutta methods with explicit stages for differential-algebraic systems of index 2
TL;DR: The construction of higher order methods is simplified substantially by a slight modification of the Runge-Kutta method combined with an improved strategy for the computation of the algebraic solution components.
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A finite element model of a 3D dry revolute joint incorporated in a multibody dynamic analysis
TL;DR: A prehensive assessment of the current contact force models implemented in the MultiBody Dynamics (MBD) approach is performed, validating the need of a new model that is able to evaluate with accuracy the contact forces obtained, and a benchmark problem is presented through a 3D slider–crank mechanism.
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A four stages numerical pair with optimal phase and stability properties
Vladislav N. Kovalnogov,Ruslan V. Fedorov,Viktor M. Golovanov,Boris M. Kostishko,T. E. Simos +4 more
TL;DR: In this article, for the first time in the literature, a new numerical pair has been obtained, which is used for the solution of coupled Schrodinger equations, and the properties of the new pair are analyzed.
References
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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.
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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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