RKDP87 (Dormand-Prince)

class pathsim.solvers.rkdp87.RKDP87(*solver_args, **solver_kwargs)[source]

Bases: ExplicitRungeKutta

Dormand-Prince 8(7) pair (DOP853). Thirteen stages, 8th order with embedded 7th order error estimate.

The highest-order general-purpose explicit pair in this library. Has the FSAL property (not exploited in this implementation).

Characteristics

  • Order: 8 (propagating) / 7 (embedded)

  • Stages: 13

  • Explicit, adaptive timestep

Note

Only worthwhile when the dynamics are very smooth and tolerances are extremely tight (roughly \(10^{-10}\) or below). The 13 function evaluations per step are expensive, but the 8th order convergence means the step size can be much larger than with lower-order methods at the same error. Suitable for generating reference solutions to validate other solvers in a block diagram. For typical engineering tolerances (\(10^{-4}\)–\(10^{-8}\)), RKDP54 or RKV65 are more efficient.

References