DIRK3

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

Bases: DiagonallyImplicitRungeKutta

Four-stage, 3rd order L-stable DIRK method. Stiffly accurate.

L-stability (\(|R(\infty)| = 0\)) fully damps parasitic high-frequency modes. The stiffly accurate property ensures the last stage equals the step output, which is beneficial for differential-algebraic systems.

Characteristics

  • Order: 3

  • Stages: 4 (implicit)

  • Fixed timestep

  • L-stable, stiffly accurate

Note

A robust fixed-step solver for stiff block diagrams. L-stability makes it well-suited for systems with widely separated time scales, such as a fast electrical subsystem driving a slow thermal or mechanical model. Also used internally as the startup method for BDF solvers. For adaptive stepping on stiff problems, prefer ESDIRK43.

References