pathsim.solvers.esdirk43 module

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

Bases: DiagonallyImplicitRungeKutta

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

Features an embedded 3rd order method for adaptive step size control. The first stage is explicit. L-stable and stiffly accurate, making it excellent for stiff problems requiring moderate-to-high accuracy with adaptive timestepping.

Characteristics

• Order: 4

• Embedded Order: 3

• Stages: 6 (1 Explicit, 5 Implicit)

• Implicit (ESDIRK)

• Adaptive timestep

• L-stable

• Stiffly accurate

When to Use

• Stiff problems with adaptive stepping: Excellent default for stiff ODEs

• Moderate-to-high accuracy: 4th order with good error control

• Damping high frequencies: L-stability damps spurious oscillations

• General-purpose stiff solver: Reliable choice for most stiff applications

Recommended as a default adaptive stiff solver. For very high accuracy, use ESDIRK54. For non-stiff problems, RKDP54 is more efficient.

References

[1]

Kennedy, C. A., & Carpenter, M. H. (2019). “Diagonally implicit Runge-Kutta methods for stiff ODEs”. Applied Numerical Mathematics, 146, 221-244.

[2]

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