SSPRK34

class pathsim.solvers.ssprk34.SSPRK34(*solver_args, **solver_kwargs)[source]

Bases: ExplicitRungeKutta

Four-stage, 3rd order Strong Stability Preserving (SSP) explicit Runge-Kutta method.

Provides a larger stability region and higher SSP coefficient compared to SSPRK33, particularly along the negative real axis, at the cost of an additional stage. Useful when stability is more critical than computational cost for a 3rd order explicit method.

Characteristics

  • Order: 3

  • Stages: 4

  • Explicit (SSP)

  • Fixed timestep only

  • SSP coefficient: \(C = 2\)

  • Enhanced stability compared to SSPRK33

When to Use

  • Larger timesteps: SSP coefficient of 2 allows larger stable timesteps

  • Difficult hyperbolic problems: More robust than SSPRK33 for challenging cases

  • Extra stability needed: When SSPRK33 exhibits instabilities

  • Worth extra stage: When the improved stability justifies 4 stages vs 3

Trade-off: More expensive than SSPRK33 but allows larger timesteps and better stability. Use when stability is critical.

References