ESDIRK4

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

Bases: DiagonallyImplicitRungeKutta

Six-stage, 4th order Singly Diagonally Implicit Runge-Kutta (ESDIRK) method.

Features an explicit first stage (making it ESDIRK). This specific tableau is designed for handling stiff problems and potentially Differential Algebraic Equations (DAEs) of index up to two or three. Does not have an embedded method for error estimation in this implementation (fixed step only).

Characteristics

• Order: 4

• Stages: 6 (1 Explicit, 5 Implicit)

• Implicit (ESDIRK)

• Fixed timestep only

• A-stable

When to Use

• Stiff problems with fixed timestep: 4th order accuracy for stiff ODEs

• Differential-algebraic equations: Suitable for DAEs of index 2-3

• Moderate-to-high accuracy on stiff problems: Better than 3rd order methods

• Known stable timestep: When adaptive stepping is not needed

Note: For adaptive timestepping on stiff problems, use ESDIRK43 or ESDIRK54 instead.

References

[1]

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

[2]

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