RKF78 (Fehlberg)

class pathsim.solvers.rkf78.RKF78(*solver_args, **solver_kwargs)

Bases: ExplicitRungeKutta

Runge-Kutta-Fehlberg 7(8) pair. Thirteen stages, 7th order propagation with 8th order error estimate.

Characteristics

• Order: 7 (propagating) / 8 (error estimate)

• Stages: 13

• Explicit, adaptive timestep

Note

One of the earliest very-high-order embedded pairs. At the same stage count, the Dormand-Prince pair (RKDP87) generally provides better error constants. Consider RKDP87 for new work unless Fehlberg-pair compatibility is required.

References

[1]

Fehlberg, E. (1968). “Classical fifth-, sixth-, seventh-, and eighth-order Runge-Kutta formulas with stepsize control”. NASA Technical Report TR R-287.

[2]

Hairer, E., Nørsett, S. P., & Wanner, G. (1993). “Solving Ordinary Differential Equations I: Nonstiff Problems”. Springer Series in Computational Mathematics, Vol. 8. :doi:`10.1007/978-3-540-78862-1`