pathsim.solvers.rkf78 module

class pathsim.solvers.rkf78.RKF78(*solver_args, **solver_kwargs)[source]

Bases: ExplicitRungeKutta

Thirteen-stage, 7th order explicit Runge-Kutta-Fehlberg method.

Features an embedded 8th order method for error estimation. The difference provides an 8th order error estimate. The 7th order solution is typically propagated. Designed for very high accuracy requirements and long-time integration where precision is critical.

Characteristics

  • Order: 7 (Propagating solution)

  • Embedded Order: 8 (Error estimation)

  • Stages: 13

  • Explicit

  • Adaptive timestep

  • Very high accuracy, nearly symplectic properties

When to Use

  • Very high accuracy needs: When stringent error tolerances are essential

  • Long-time integration: Problems requiring stable, accurate integration over long periods

  • Smooth dynamics: Highly smooth problems where high order is efficient

  • Scientific precision: Astronomical calculations, molecular dynamics, precision engineering

Note

Expensive per step (13 stages), but can take very large steps with tight tolerances. Not suitable for non-smooth problems or when function evaluations are expensive.

References