RKBS32 (Bogacki-Shampine)

class pathsim.solvers.rkbs32.RKBS32(*solver_args, **solver_kwargs)[source]

Bases: ExplicitRungeKutta

Four-stage, 3rd order explicit Runge-Kutta method by Bogacki and Shampine.

Features an embedded 2nd order method for adaptive step size control with FSAL (First Same As Last) property. The 3rd order result is used for propagation. Commonly used in software packages (e.g., MATLAB’s ode23). Good for problems requiring low to moderate accuracy with efficiency.

Characteristics

  • Order: 3 (Propagating solution)

  • Embedded Order: 2 (Error estimation)

  • Stages: 4 (3 effective due to FSAL)

  • Explicit

  • Adaptive timestep

  • Efficient low-to-moderate accuracy solver

When to Use

  • Low-to-moderate accuracy needs: When stringent accuracy is not required

  • Efficiency-focused applications: Cheaper than 5th order methods

  • Smooth non-stiff problems: Well-suited for mildly nonlinear problems

  • Default low-order adaptive solver: Good general-purpose choice for less demanding problems

Note

More efficient than 5th order methods but less accurate. For higher accuracy requirements, use RKDP54 or RKCK54. Nonetheless a good default explicit adaptive timestep solver.

References