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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A mechanistic model of coral bleaching due to temperature-mediated light-driven reactive oxygen build-up in zooxanthellae
Mark E. Baird,Mathieu Mongin,Farhan Rizwi,Line K. Bay,Neal E. Cantin,Monika Soja-Woźniak,J Skerratt +6 more
TL;DR: In this article, a model of the coral-symbiont relationship was developed to consider temperature-mediated build-up of reactive oxygen species due to excess light, leading to zooxanthellae expulsion.
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Bubbleprofiler: Finding the field profile and action for cosmological phase transitions
Peter Athron,Csaba Balázs,Michael Hugh Bardsley,Andrew Fowlie,Andrew Fowlie,Dylan Harries,Dylan Harries,Graham White,Graham White +8 more
TL;DR: BubbleProfiler as mentioned in this paper is a C++ software package for finding field profiles in bubble walls and calculating the bounce action during phase transitions involving multiple scalar fields using a recently proposed perturbative method for potentials with multiple fields and a shooting method for single field cases.
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Observation and quantification of inertial effects on the drift of floating objects at the ocean surface
María J. Olascoaga,Francisco J. Beron-Vera,P. Miron,Joaquin Trinanes,Joaquin Trinanes,Joaquin Trinanes,Nathan F. Putman,Rick Lumpkin,Gustavo Goni +8 more
TL;DR: In this paper, the authors present results from an experiment designed to better understand the mechanism by which ocean currents and winds control flotsam drift, and explain the differences in the trajectories described by the special drifters as a result of their inertia, primarily buoyancy.
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Modeling of External Filter Cake Build-up in Radial Geometry
TL;DR: In this paper, a model has been developed to describe the steady state external filter cake thickness profile along the wellbore, which is derived from the force balance for a deposited particle on the cake surface and the volume conservation of the fluid in the well-bore.
Relationship Between Left Ventricular and Arterial System Elastances
TL;DR: The arterial system, in terms of elastance, is dynamically and temporally coupled to the left-ventricle during ejection.
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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