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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Adaptive stiff solvers at low accuracy and complexity
TL;DR: This paper proposes to use a monitor function defined by comparing a measure of the local variability of the solution times the used step size and the order of magnitude of the solutions instead of the classical approach based on some local error estimation for the adaptive algorithm.
Journal ArticleDOI
Experimental analysis and modeling of internal combustion engine operating with wet ethanol
Weslei Monteiro Ambrós,Thompson Lanzanova,J.L.S. Fagundez,Rafael Lago Sari,Damaris Kirsch Pinheiro,Mario Eduardo Santos Martins,Nina P.G. Salau +6 more
TL;DR: In this paper, a mathematical model was proposed to predict the effect that the use of wet ethanol has on the performance of internal combustion engines, along with experimental data, which showed good ability to predict engine performance based on the variations of power, torque, conversion efficiency and specific fuel consumption.
Journal ArticleDOI
Application of Robust Control Tools to the Simultaneous Design and Control of Dynamic Systems
TL;DR: In this paper, the simultaneous design and control problem is posed as a nonlinear constrained optimization problem and compared to the design of a mixing tank process using a dynamic optimization approach, and the expected computational burden required by this method for large-scale processes is also estimated.
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Modeling of Nociceptor Transduction in Skin Thermal Pain Sensation
TL;DR: A model of nociceptor transduction in skin thermal pain is developed in order to build direct relationship between stimuli and neural response, which incorporates a skin thermomechanical model for the calculation of temperature, damage and thermal stress at the location of nocentre and a revised Hodgkin-Huxley form model for frequency modulation.
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Visual Analysis of Cardiac 4D MRI Blood Flow Using Line Predicates
TL;DR: This work applies a visual analysis method using line predicates to 4D MRI data of healthy and pathological hearts and presents several flow aspects that could not be shown with current methods.
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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