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 cell-size threshold limits cell polarity and asymmetric division potential
Lars Hubatsch,Florent Peglion,Jacob D. Reich,Nelio T. L. Rodrigues,Nisha Hirani,Rukshala Illukkumbura,Nathan W. Goehring,Nathan W. Goehring +7 more
TL;DR: Using the stem cell-like germ lineage of the C. elegans embryo as a model, it is found that the behaviour of PAR proteins fails to scale with cell size, and theoretical analysis demonstrates that this lack of scaling results in a size threshold below which polarity is destabilized, yielding an unpolarized system.
Journal ArticleDOI
Runge–Kutta type methods with special properties for the numerical integration of ordinary differential equations
TL;DR: This work reviews single step methods of the Runge–Kutta type with special properties specially tuned to integrate problems that exhibit a pronounced oscillatory character and such problems arise often in celestial mechanics and quantum mechanics.
Journal ArticleDOI
A fully coupled space-time multiscale modeling framework for predicting tumor growth.
TL;DR: A fully coupled space-time multiscale framework for modeling tumor growth is developed and is capable of predicting major characteristics of tumor growth such as the morphological instability, growth patterns of different cell phenotypes, compact regions of the higher cell density at the tumor region, and the reduction of growth rate due to drug delivery.
Journal ArticleDOI
Realistic Earth escape strategies for solar sailing
TL;DR: In this paper, the authors investigated seasonal variations in sail escape times from Earth orbit and corroborated within a numerical trajectory model, and presented a set of blended-sail control algorithms, explicitly independent of time, which provided near-optimal escape trajectories and maintained a safe minimum altitude.
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A tool for neutrophil guided dose adaptation in chemotherapy
TL;DR: This paper describes the transfer of a previously developed semi-mechanistic model for myelosuppression from NONMEM to a dosing tool in MS Excel, which proved capable to solve a differential equation system describing the pharmacokinetics and pharmacodynamics, with estimation performance comparable to NONM EM.
References
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Journal ArticleDOI
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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