RKF45 (Fehlberg)

class pathsim.solvers.rkf45.RKF45(*solver_args, **solver_kwargs)

Bases: ExplicitRungeKutta

Runge-Kutta-Fehlberg 5(4) pair. Six stages, 5th order propagation with an embedded 4th order solution for local error estimation (local extrapolation, matching the RKCK54 / RKDP54 convention).

The historically first widely-used embedded pair for automatic step-size control. The 5th order solution b5 is propagated; the difference to the 4th order solution b4 (TR = b5 - b4) provides a local error estimate of the lower-order result.

Characteristics

• Order: 5 (propagating) / 4 (error estimate)

• Stages: 6

• Explicit, adaptive timestep

Note

Largely superseded by the Dormand-Prince (RKDP54) and Cash-Karp (RKCK54) pairs, which achieve better accuracy per function evaluation on most problems. Still useful for reproducing legacy results or when comparing against published benchmarks that used RKF45.

References

[1]

Fehlberg, E. (1969). “Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems”. NASA Technical Report TR R-315.

[2]

Fehlberg, E. (1970). “Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme”. Computing, 6(1-2), 61-71. :doi:`10.1007/BF02241732`