pathsim.solvers.dirk3 module

class pathsim.solvers.dirk3.DIRK3(*solver_args, **solver_kwargs)[source]

Bases: DiagonallyImplicitRungeKutta

Four-stage, 3rd order, L-stable Diagonally Implicit Runge-Kutta (DIRK) method.

L-stability (A-stability and stiffly accurate, i.e., \(|R(\infty)| = 0\)) makes this method suitable for stiff problems where damping of high-frequency components is desired.

(Butcher tableau often attributed to Crouzeix, or Nørsett-Thomsen based on Wikipedia/Hairer).

Characteristics:

  • Order: 3

  • Stages: 4 (Implicit)

  • Implicit (DIRK)

  • Fixed timestep only

  • L-stable (and thus A-stable)