RKF45 (Fehlberg)

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

Bases: ExplicitRungeKutta

Six-stage, 4th order explicit Runge-Kutta-Fehlberg method.

Features an embedded 5th order method. The difference between the 5th and 4th order results provides a 5th order error estimate. Typically, the 4th order solution is propagated (local extrapolation available). A classic adaptive step size method, though often superseded in efficiency by Dormand-Prince methods.

Characteristics

• Order: 4 (Propagating solution)

• Embedded Order: 5 (Error estimation)

• Stages: 6

• Explicit

• Adaptive timestep

• Classic adaptive method, good for moderate accuracy

When to Use

• Moderate accuracy requirements: Good balance for many engineering applications

• Well-established benchmarks: When comparing against historical results

• Non-stiff smooth problems: Standard choice for a wide range of ODEs

Note

While this is a classic method, RKDP54 or RKCK54 generally offer better efficiency for the same computational cost. Consider RKDP54 or RKCK54 for new applications unless specific properties of RKF45 are required.

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.

[3]

Hairer, E., Nørsett, S. P., & Wanner, G. (1993). “Solving Ordinary Differential Equations I: Nonstiff Problems”. Springer Series in Computational Mathematics, Vol. 8.