Runge–Kutta–Fehlberg method
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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(h4) method together with an O(h5) 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 very efficient for ordinary problems of numerical integration. [1]
[edit] Notes
- ^ 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.
[edit] 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.
