pathsim.solvers.rkv65 module

class pathsim.solvers.rkv65.RKV65(*solver_args, **solver_kwargs)[source]

Bases: ExplicitRungeKutta

Nine-stage, 6th order explicit Runge-Kutta method by Verner.

Features an embedded 5th order method for adaptive step size control. This is the ‘most robust’ 9-stage 6(5) pair from Jim Verner’s collection, designed for efficient high-accuracy integration of non-stiff problems. Offers better accuracy than 5th order methods while being more efficient than 8th order methods.

Characteristics

  • Order: 6 (Propagating solution)

  • Embedded Order: 5

  • Stages: 9

  • Explicit

  • Adaptive timestep

  • Efficient high-order method for non-stiff problems

When to Use

  • High-accuracy requirements: When 5th order is insufficient but 8th order is overkill

  • Smooth non-stiff problems: Excellent for problems with smooth solutions

  • Stringent error tolerances: When tight tolerances are needed efficiently

  • Scientific computing: Common in astronomical and molecular dynamics simulations

Note

More expensive per step than 5th order methods, but can take larger steps for the same accuracy. For very high accuracy, consider RKF78 or RKDP87.

References