RKF21 (Fehlberg)

class pathsim.solvers.rkf21.RKF21(*solver_args, **solver_kwargs)

Bases: ExplicitRungeKutta

Three-stage, 2nd order embedded Runge-Kutta-Fehlberg method.

Features an embedded 1st order method for adaptive step size control. This is a classic low-order adaptive method. The three stages make it computationally cheap, but the low order limits accuracy. The error estimate is also less accurate than higher-order methods.

Characteristics

• Order: 2 (Propagating solution)

• Embedded Order: 1 (Error estimation)

• Stages: 3

• Explicit

• Adaptive timestep

• Efficient but low accuracy

When to Use

• Computationally cheap adaptive stepping: When you need some adaptive control but minimal cost

• Coarse integration: Problems where high accuracy is not required

• Event detection: When timestep is limited by events rather than truncation error

• Initial exploration: Quick preliminary runs before using higher-order methods

Note

Low accuracy. For most applications requiring adaptive stepping, RKBS32 or RKDP54 are better choices.

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]

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