scispace - formally typeset
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.
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
More filters
Posted Content

Exact Simulation of Wishart Multidimensional Stochastic Volatility Model

Chulmin Kang, +1 more
- 02 Sep 2013 - 
TL;DR: An exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al, is proposed, based on analysis of the conditional characteristic function of the log-price given volatility level.
Journal ArticleDOI

Comparison of diagonal-implicit, linear-implicit and half-explicit Runge–Kutta methods in non-linear finite element analyses

Steffen Rothe, +3 more
- 03 Feb 2012 - 
TL;DR: It turns out that for models where linear elasticity is one ingredient in the constitutive model, the method leads to only one required LU-decomposition at the beginning of the entire computation, and in each time step, this outperforms current finite element computations.

Limit cycle oscillation prediction for aeroelastic systems with discrete bilinear stiffness

Gareth A. Vio, +1 more
TL;DR: In this article, a methodology is presented that enables the prediction of the limit cycle oscillation behavior of aeroelastic systems with discrete cubic structural nonlinearities using the center manifold and normal form approaches.
Journal ArticleDOI

Adaptive ODE solvers in extended Kalman filtering algorithms

Maria V. Kulikova, +1 more
- 01 May 2014 - 
TL;DR: This paper studies numerical methods that are used to treat ordinary differential equations arising in extended Kalman filtering algorithms, and shows that built-in Matlab ODE solvers are not able to cope with a number of tests considered here.
Journal ArticleDOI

Numerical Studies Using Full Car Model for Combined Primary and Cabin Suspension

S.K. Sharma, +3 more
- 01 Jan 2016 - 
TL;DR: In this article, a 10 degree of freedom full car model with integration of primary and cabin suspension in the Simulink environment to see the effect of cabin suspension on the ride comfort over the primary suspension system is presented.
References
More filters
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.