ESDIRK85

class pathsim.solvers.esdirk85.ESDIRK85(*solver_args, **solver_kwargs)[source]

Bases: DiagonallyImplicitRungeKutta

Sixteen-stage, 8th order ESDIRK method with embedded 5th order error estimate. L-stable and stiffly accurate (ESDIRK(16,8)[2]SAL-[(16,5)]).

Characteristics

  • Order: 8 (propagating) / 5 (embedded)

  • Stages: 16 (1 explicit, 15 implicit)

  • Adaptive timestep

  • L-stable, stiffly accurate

  • Stage order 2

Note

Fifteen implicit solves per step make this very expensive. It is only justified when the right-hand side evaluation is itself costly (large state dimension, expensive ODE blocks) and very tight tolerances are required so that the 8th order convergence compensates through much larger steps. For generating stiff reference solutions to validate other solvers. In almost all practical block-diagram simulations, ESDIRK54 is the better choice.

References