ESDIRK32

class pathsim.solvers.esdirk32.ESDIRK32(*solver_args, **solver_kwargs)

Bases: DiagonallyImplicitRungeKutta

Four-stage, 3rd order Embedded Singly Diagonally Implicit Runge-Kutta (ESDIRK) method.

Features an embedded 2nd order method for adaptive step size control. The first stage is explicit, making the method suitable for problems with explicit first stages. Designed to be applicable to index-2 Differential Algebraic Equations (DAEs).

Characteristics

• Order: 3

• Embedded Order: 2

• Stages: 4 (1 Explicit, 3 Implicit)

• Implicit (ESDIRK)

• Adaptive timestep

• A-stable

When to Use

• Moderately stiff problems with adaptivity: Good for stiff ODEs needing timestep control

• Differential-algebraic equations: Suitable for DAEs of index up to 2

• Entry-level adaptive implicit: Lower-order adaptive implicit method

• Testing stiffness: Explore if a problem requires implicit methods

Trade-off: Lower accuracy than ESDIRK43 or ESDIRK54, but computationally cheaper. For higher accuracy, use ESDIRK54.

References

[1]

Williams, D. M., Houzeaux, G., Aubry, R., Vázquez, M., & Calmet, H. (2013). “Efficiency of a matrix-free linearly implicit time integration strategy”. Computers & Fluids, 83, 77-89.

[2]

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

[3]

Hairer, E., & Wanner, G. (1996). “Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems”. Springer Series in Computational Mathematics, Vol. 14.