pathsim.solvers.dirk2 module

class pathsim.solvers.dirk2.DIRK2(*solver_args, **solver_kwargs)[source]

Bases: DiagonallyImplicitRungeKutta

Two-stage, 2nd order, Diagonally Implicit Runge-Kutta (DIRK) method.

This specific method is SSP-optimal (largest radius of absolute monotonicity for a 2-stage, 2nd order DIRK), symplectic, and A-stable. It’s a robust choice for moderately stiff problems where second-order accuracy is sufficient.

FROM:

L. Ferracina and M.N. Spijker. Strong stability of singly-diagonally-implicit Runge-Kutta methods. Applied Numerical Mathematics, 58:1675–1686, 2008.

Characteristics:

  • Order: 2

  • Stages: 2 (Implicit)

  • Implicit (DIRK)

  • Fixed timestep only

  • A-stable, SSP-optimal, Symplectic