DIRK3

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. The stiffly accurate property ensures good behavior for problems with singular perturbations and differential-algebraic equations.

Characteristics

  • Order: 3

  • Stages: 4 (Implicit)

  • Implicit (DIRK)

  • Fixed timestep only

  • L-stable (and thus A-stable)

  • Stiffly accurate

When to Use

  • Stiff problems: Excellent stability for very stiff ODEs

  • Damping required: L-stability damps high-frequency oscillations

  • Differential-algebraic equations: Stiffly accurate property helps with DAEs

  • 3rd order implicit: Moderate accuracy with strong stability

Recommended for stiff problems requiring 3rd order accuracy. For higher order, consider ESDIRK54. For variable timestep, use adaptive ESDIRK methods.

References