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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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Finite-size Lagrangian coherent structures in a two-sided lid-driven cavity

Francesco Romanò, +2 more
TL;DR: In this article, a Lagrangian coherent structure can arise in dilute suspensions solely because of the size of the particles and when moving near boundaries, a lubrication-induced drag transfers the particles from the chaotic sea of the unperturbed fluid flow to particular Kolmogorov-Arnold-Moser tori.
Journal ArticleDOI

A complete in phase FiniteDiffrnc algorithm for DiffrntEqutins in chemistry

Chia Liang Lin, +1 more
- 01 Jun 2020 - 
TL;DR: In this article, a new FiniteDiffrnc process is introduced or the effectual solution of the DiffrntEqutins in Chemistry in order to solve the Finite Difference problem.
Journal ArticleDOI

A novel formulation for integrating nonlinear kinematic hardening Drucker-Prager’s yield condition

Mohammad Rezaiee-Pajand, +1 more
- 01 Jan 2012 - 
TL;DR: In this paper, the Drucker-Prager model obeying nonlinear kinematic and linear isotropic hardenings is considered and a new integration formulation is suggested that is based on definitions of angles between the strain rate and the shifted stress, and between shifted stress and back stress in the deviatoric plane.
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New five-stages two-step method with improved characteristics

Junfeng Yao, +1 more
- 19 Feb 2018 - 
TL;DR: In this article, a new five-stages symmetric two-step method with improved characteristics is developed, which is based on the numerical solution of systems of coupled differential equations of the Schrodinger type.
Journal ArticleDOI

Does abnormal spinal reciprocal inhibition lead to co-contraction of antagonist motor units? A modeling study.

Vassilis Cutsuridis
- 01 Jan 2007 - 
TL;DR: Simulation results show that although reciprocal inhibition is reduced in DA depleted case, it doesn't lead to co-contraction of antagonist motor neurons, and implications to Parkinsonian rigidity are discussed.
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.