RKDP54 (Dormand-Prince)

class pathsim.solvers.rkdp54.RKDP54(*solver_args, **solver_kwargs)[source]

Bases: ExplicitRungeKutta

Seven-stage, 5th order explicit Runge-Kutta method by Dormand and Prince (DOPRI5).

Features an embedded 4th order method. Widely considered one of the most efficient general-purpose adaptive step size solvers for non-stiff problems requiring moderate to high accuracy. The 5th order result is used for propagation. Used as the basis for MATLAB’s ode45. FSAL property (not available in this implementation).

Characteristics

  • Order: 5 (Propagating solution)

  • Embedded Order: 4

  • Stages: 7 (6 effective due to FSAL, not here though)

  • Explicit

  • Adaptive timestep

  • Industry-standard adaptive solver

When to Use

  • Default adaptive solver: Excellent first choice for most non-stiff problems

  • Moderate-to-high accuracy: 5th order provides good accuracy efficiently

  • General-purpose integration: Reliable for a wide variety of ODE systems

  • Industry standard: Well-tested and widely used in production software

Note

Recommended as the primary adaptive solver for non-stiff problems. For stiff problems, use BDF or ESDIRK methods. For very high accuracy, consider RKV65 or RKDP87.

References