Runge–Kutta–Fehlberg method
- Runge–Kutta–Fehlberg method
In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is a method for the numerical solution of ordinary differential equations developed by the German mathematician Erwin Fehlberg. Based on the Runge–Kutta methods, the Fehlberg method uses an O("h"4) method together with an O("h"5) method, and hence is often referred to as RKF45. By performing one extra calculation (as compared to RK5), a more appropriate step size is determined, making this method efficient for ordinary problems of numerical integration. [According to Hairer et al. (1993, §II.4), the method was originally proposed in Fehlberg (1969); Fehlberg (1970) is an extract of the latter publication.]
The Butcher tableau is:
The first row of "b" coefficients gives the fourth-order accurate solution, and the second row has order five.
Notes
References
* Erwin Fehlberg (1969). "Low-order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems". NASA Technical Report 315.
* Erwin Fehlberg (1970). "Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme," "Computing (Arch. Elektron. Rechnen)", vol. 6, pp. 61–71.
* Ernst Hairer, Syvert Nørsett, and Gerhard Wanner (1993). "Solving Ordinary Differential Equations I: Nonstiff Problems", second edition, Springer-Verlag, Berlin. ISBN 3-540-56670-8.
External links
* [http://math.fullerton.edu/mathews/n2003/RungeKuttaFehlbergMod.html RKF45 computer programs] (see also [http://math.fullerton.edu/mathews/n2003/rungekuttafehlberg/RungeKuttaFehlbergProof.pdf] )
Wikimedia Foundation.
2010.
Look at other dictionaries:
Método de Runge-Kutta — El método de Runge Kutta es un método genérico de resolución numérica de ecuaciones diferenciales. Este conjunto de métodos fue inicialmente desarrollado alrededor del año 1900 por los matemáticos C. Runge y M. W. Kutta. Contenido 1 Descripción 1 … Wikipedia Español
Dormand–Prince method — In numerical analysis, the Dormand–Prince method, or DOPRI method, is a method for solving ordinary differential equations (Dormand Prince 1980). The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six… … Wikipedia
Cash–Karp method — In numerical analysis, the Cash–Karp method is a method for solving ordinary differential equations (ODEs). The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth… … Wikipedia
List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra … Wikipedia
List of mathematics articles (R) — NOTOC R R. A. Fisher Lectureship Rabdology Rabin automaton Rabin signature algorithm Rabinovich Fabrikant equations Rabinowitsch trick Racah polynomials Racah W coefficient Racetrack (game) Racks and quandles Radar chart Rademacher complexity… … Wikipedia
Método de Dormand-Prince — En análisis numérico, Dormand Prince es un método para la resolución de ecuaciones diferenciales ordinarias. Pertenece a la familia de métodos Runge Kutta. Evalúa seis veces la función para calcular las soluciones de cuarto y quinto orden. La… … Wikipedia Español
Numerical ordinary differential equations — Illustration of numerical integration for the differential equation y = y,y(0) = 1. Blue: the Euler method, green: the midpoint method, red: the exact solution, y = et. The step size is h = 1.0 … Wikipedia
Adaptive stepsize — is a technique in numerical analysis used for many problems, but mainly for integration; This can be normal integration (that is quadrature ), or the process of solving an ordinary differential equation. This article focuses on the latter. For an … Wikipedia
