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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.
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.

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Citations
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Journal ArticleDOI

RBF-PS scheme for solving the equal width equation

Marjan Uddin
- 01 Oct 2013 - 
TL;DR: The equal width equation is solved by a RBF-PS scheme, and the radial kernels are used to transform the PDE into a system of ODEs.
Journal ArticleDOI

Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems

Slimane Adjerid, +1 more
- 25 Jan 2011 - 
TL;DR: An a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions and asymptotically exact estimates of the finite element error are presented.
Journal ArticleDOI

A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

Ibraheem Alolyan, +2 more
- 01 Mar 2011 - 
TL;DR: In this paper, a family of algebraic order eight-step methods for the numerical solution of the one dimensional Schrodinger equation is presented, and the efficiency of the new methodology is proved via theoretical analysis and numerical applications.
Journal ArticleDOI

Implementation of an Adaptive BDF2 Formula and Comparison with the MATLAB Ode15s

E. Alberdi Celaya, +2 more
TL;DR: This work has focused on the second order accurate and unconditionally stable BDF (BDF2) and implemented a real adaptive step size BDF2 algorithm using the same strategy as the B DF2 implemented in the ode15s, resulting the new algorithm more efficient than the one implemented in MATLAB.
Journal ArticleDOI

Parameter estimation of influenza epidemic model

Md. Samsuzzoha, +2 more
- 01 Sep 2013 - 
TL;DR: SEIRS and SVEIRS epidemic models are considered here to capture the main characteristic of transmission of influenza epidemic governed by a system of differential equations and reflect considerably the dynamical behavior of the influenza epidemic field data used.
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.