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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Nonlinear heat transfer processes in a two-phase thermofluidic oscillator
TL;DR: In this paper, a nonlinear model for a two-phase thermofluidic oscillator was proposed and compared to those from the linear equivalents and experimental observations, and the results reveal that although both linear and nonlinear models predict similar oscillation frequencies, the nonlinear approach predicts lower exergetic efficiencies.
Journal ArticleDOI
Identification and quantification of stick-slip induced brake groan events using experimental and analytical investigations.
TL;DR: In this article, a lumped torsional model is employed to approximate the dynamics of the real mechanical system, assigning inertia to the drive, brake rotor, brake caliper and tire/vehicle, and by appropriate algorithms the simulation time histories include the effects of the friction nonlinearity coupling brake and rotor.
Journal ArticleDOI
Accurately closed newton–cotes trigonometrically-fitted formulae for the numerical solution of the schrödinger equation
T. E. Simos,T. E. Simos +1 more
TL;DR: In this article, a trigonometrically-fitted high-order closed Newton-Cotes formula was proposed to solve the resonance problem of the radial Schrodinger equation.
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An adaptive parallel tempering method for the dynamic data-driven parameter estimation of nonlinear models
TL;DR: An adaptive parallel tempering algorithm is developed in a user-friendly fashion that efficiently and robustly generates near-optimum solutions and is extensively validated through its application to a number of algebraic and dynamic global optimization problems from Chemical Engineering literature.
Journal ArticleDOI
Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential
M. Geilhufe,Steven Achilles,Markus A. Köbis,Martin Arnold,Ingrid Mertig,Ingrid Mertig,Wolfram Hergert,Arthur Ernst +7 more
TL;DR: The implementation of the Korringa-Kohn-Rostoker Green function method is tested and exemplarily demonstrated for a spherically symmetric treatment of a Coulomb potential and for a Mathieu potential to cover the full-potential implementation.
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.
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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