ESDIRK4

class pathsim.solvers.esdirk4.ESDIRK4(*solver_args, **solver_kwargs)

Bases: DiagonallyImplicitRungeKutta

Six-stage, 4th order ESDIRK method. L-stable and stiffly accurate.

No embedded error estimator; fixed timestep only.

Characteristics

• Order: 4

• Stages: 6 (1 explicit, 5 implicit)

• Fixed timestep

• L-stable, stiffly accurate

• Stage order 2

Note

Provides 4th order accuracy on stiff block diagrams when the timestep is predetermined (e.g. real-time or hardware-in-the-loop contexts). The explicit first stage reuses the last function evaluation from the previous step, saving one implicit solve per step compared to a fully implicit DIRK. L-stability and stiff accuracy ensure full damping of parasitic high-frequency modes. For adaptive stepping, use ESDIRK43 which adds an embedded error estimator at the same stage count.

References

[1]

Kennedy, C. A., & Carpenter, M. H. (2016). “Diagonally implicit Runge-Kutta methods for ordinary differential equations. A review”. NASA/TM-2016-219173.

[2]

Hairer, E., & Wanner, G. (1996). “Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems”. Springer Series in Computational Mathematics, Vol. 14. :doi:`10.1007/978-3-642-05221-7`