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
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Emerging investigators series: building a theory for smart stormwater systems
Abstract: Retrofitting stormwater systems with sensors and controllers will allow cities to be operated as real-time, distributed treatment plants. Unlike static infrastructure, which cannot adapt its operation to individual storms or changing land uses, “smart” stormwater systems will use system-level coordination to maximize watershed pollutant removal and treatment. We illustrate that this vision is not limited by technology, which has matured to the point at which it can be ubiquitously deployed. Rather, the challenge is much more fundamental and rooted in a system-level understanding of environmental science. Once distributed stormwater systems become highly instrumented and controlled, how should they be operated to achieve desired watershed outcomes? The answer to this question demands the development of a theoretical framework for smart stormwater systems. In this paper, we lay out the requirements for such a theory. Acknowledging that the adoption of these systems may still be years away, we also present a modeling framework to allow for the simulation of controlled stormwater systems before they become commonplace. We apply this control framework to two simulated case studies in which stormwater sites are controlled to reduce nitrate loads to downstream water bodies.
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Chain length dependent olefin re-adsorption model for Fischer–Tropsch synthesis over Co-Al2O3 catalyst
TL;DR: In this article, a comprehensive kinetic model for the Fischer-Tropsch synthesis over Co/Al 2 O 3 catalyst, was developed to provide mechanistic explanations for deviations from Anderson-Schulz Flory (ASF) distributions.
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A predictor–corrector explicit four-step method with vanished phase-lag and its first, second and third derivatives for the numerical integration of the Schrödinger equation
TL;DR: In this article, a predictor-corrector explicit four-step method of sixth algebraic order is investigated, and the results of the elimination of the phase-lag and its first, second and third derivatives on the efficiency of the proposed method are investigated theoretically and computationally.
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Alfvén solitons in a Fermionic quantum plasma
TL;DR: Coupled Zakharov-type equations are derived for circularly polarized Alfvén waves which show that variations in density take the form of dressed density solitons in which an approximately Gaussian peak is surrounded by smaller sinusoidal variations in the density envelope.
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Investigation of moving fixture on deformation suppression during milling process of thin-walled structures
TL;DR: In this article, a machining case is implemented to demonstrate the effectiveness and feasibility of the proposed method and a dynamic model of the new cutter-workpiece-fixture system is constructed to analyze the workpiece deformation.
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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