RKDP87 (Dormand-Prince)

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

Bases: ExplicitRungeKutta

Thirteen-stage, 8th order explicit Runge-Kutta method by Dormand and Prince (DOP853).

Features an embedded 7th order method for adaptive step size control. Designed for problems requiring very high accuracy with excellent error estimation. This is one of the most efficient 8th order methods available. FSAL property (not available in this implementation).

Characteristics

  • Order: 8 (Propagating solution)

  • Embedded Order: 7

  • Stages: 13 (12 effective due to FSAL)

  • Explicit

  • Adaptive timestep

  • State-of-the-art very high-order solver

When to Use

  • Extremely high accuracy: When very tight error tolerances are required

  • Smooth high-dimensional problems: Excellent for smooth ODEs in many dimensions

  • Long-time precision integration: Orbital mechanics, celestial mechanics

  • Benchmark computations: Reference solutions for method comparison

Note

Generally recommended as the highest-order general-purpose explicit method. More efficient than RKF78 for the same accuracy level. Only use when very high accuracy justifies the 13-stage computational cost.

References