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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Efficient low computational cost hybrid explicit four-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the Schrödinger equation
TL;DR: Based on an optimized explicit four-step method, a new hybrid high algebraic order four step method is introduced in this paper, which investigates the procedure of vanishing of the phase-lag and its first, second, third and fourth derivatives.
Posted Content
Liquid Time-constant Networks
TL;DR: This work introduces a new class of time-continuous recurrent neural network models that construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates, and demonstrates the approximation capability of Liquid Time-Constant Networks (LTCs) compared to modern RNNs.
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Snakes mimic earthworms: propulsion using rectilinear travelling waves.
TL;DR: This combined experimental and theoretical study film rectilinear locomotion of three species of snakes, including red-tailed boa constrictors, Dumeril's boas and Gaboon vipers, and applies a mathematical model to show snakes have optimal wave frequencies.
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Spartan Gibbs Random Field Models for Geostatistical Applications
TL;DR: Typographical errors in certain mathematical formulas that appear in the article "Spartan Gibbs Random Field Models for Geostatistical Applications" are corrected.
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A family of explicit linear six-step methods with vanished phase-lag and its first derivative
TL;DR: In this article, a family of explicit linear six-step algebraic order 6-step methods with vanished phase-lag and its first derivative is obtained, which are computationally and theoretically more effective than other well known methods for the approximate solution of the radial Schrodinger equation and related initial value problems with periodic and/or oscillating solutions.
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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