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Open AccessJournal ArticleDOI

A family of embedded Runge-Kutta formulae

J. R. Dormand, +1 more
- 01 Mar 1980 - 
- Vol. 6, Iss: 1, pp 19-26
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.
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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.

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Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

Martin Eigel, +2 more
- 12 Feb 2018 - 
TL;DR: A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model, alleviating the 'curse of dimensionality'.
Journal ArticleDOI

Drug transport kinetics of intravascular triggered drug delivery systems.

Timo L.M. ten Hagen, +7 more
TL;DR: In this article, the authors developed a computational model to simulate IV-DDS drug delivery, for which they quantified all model parameters in vivo in rodent tumors and validated the model via quantitative intravital microscopy studies with unencapsulated fluorescent dye, and with two formulations of temperature-sensitive liposomes (slow, and fast release) encapsulating a fluorescent dye.
Journal ArticleDOI

A hybrid finite volume-finite element model for the numerical analysis of furrow irrigation and fertigation

Giuseppe Brunetti, +2 more
- 01 Jul 2018 - 
TL;DR: A hybrid Finite Volume – Finite Element (FV-FE) model is presented that describes the coupled surface-subsurface flow processes occurring during furrow irrigation and fertigation, thus reducing the dimensionality of the problem and the computational cost.
Journal ArticleDOI

Unidirectional large-amplitude oscillatory shear flow of human blood

Chaimongkol Saengow, +3 more
- 12 Nov 2019 - 
TL;DR: In this article, a new blood test, unidirectional large-amplitude oscillatory shear flow (udLAOS), was proposed to assess its non-Newtonian behaviors.
Journal ArticleDOI

Mathematical simulation and optimization of methanol dehydration and cyclohexane dehydrogenation in a thermally coupled dual-membrane reactor

Mohammad Farsi, +1 more
- 01 Nov 2011 - 
TL;DR: In this paper, a steady state heterogeneous mathematical model is developed to predict the performance of a thermally coupled dual-membrane membrane reactor for simultaneous production of hydrogen, dimethyl ether (DME) and benzene.
References
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Book

Computational Methods in Ordinary Differential Equations

John Denholm Lambert
Journal ArticleDOI

Comparing Numerical Methods for Ordinary Differential Equations

T. E. Hull, +3 more
- 01 Dec 1972 - 
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.

Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems

E. Fehlberg
Journal ArticleDOI

Coefficients for the study of Runge-Kutta integration processes

John C. Butcher
- 01 May 1963 - 
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

E. Fehlberg
TL;DR: Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.