ESDIRK43

class pathsim.solvers.esdirk43.ESDIRK43(*solver_args, **solver_kwargs)

Bases: DiagonallyImplicitRungeKutta

Six-stage, 4th order ESDIRK method with embedded 3rd order error estimate. L-stable and stiffly accurate.

Characteristics

• Order: 4 (propagating) / 3 (embedded)

• Stages: 6 (1 explicit, 5 implicit)

• Adaptive timestep

• L-stable, stiffly accurate

• Stage order 2

Note

Recommended default for stiff block diagrams. L-stability damps high-frequency parasitic modes that arise from stiff subsystems (e.g. PID controllers with large derivative gain, fast electrical or chemical dynamics). The adaptive step-size control concentrates computational effort where the solution changes rapidly. For non-stiff systems, RKDP54 avoids the implicit solve cost and is more efficient. For tighter tolerances on stiff problems, ESDIRK54 provides 5th order accuracy.

References

[1]

Kennedy, C. A., & Carpenter, M. H. (2019). “Diagonally implicit Runge-Kutta methods for stiff ODEs”. Applied Numerical Mathematics, 146, 221-244. :doi:`10.1016/j.apnum.2019.07.008`

[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`