pathsim.solvers.esdirk54 module

class pathsim.solvers.esdirk54.ESDIRK54(*solver_args, **solver_kwargs)[source]

Bases: DiagonallyImplicitRungeKutta

Seven-stage, 5th order L-stable Embedded Singly Diagonally Implicit Runge-Kutta method.

Features an embedded 4th order method for adaptive step size control. The first stage is explicit. L-stable and stiffly accurate, making it excellent for stiff problems requiring high accuracy with adaptive timestepping. This is the ESDIRK5(4)7L[2]SA2 method.

Characteristics

  • Order: 5

  • Embedded Order: 4

  • Stages: 7 (1 Explicit, 6 Implicit)

  • Implicit (ESDIRK)

  • Adaptive timestep

  • L-stable, Stiffly accurate

When to Use

  • High-accuracy stiff problems: When 5th order is needed for stiff ODEs

  • Demanding stiff applications: Chemical kinetics, combustion, atmospheric chemistry

  • Tight error tolerances: Better accuracy than 4th order methods

  • Production stiff solver: High-quality method for serious applications

Recommended for high-accuracy stiff problems. This is a state-of-the-art adaptive implicit method. For very stiff problems with less stringent accuracy, ESDIRK43 may be more efficient.

References