Backward Differentiation Formula (BDF)

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Backward Differentiation Formula (BDF)

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This is an implicit multi-step variable-order first-order derivatives method. It is Gear's backward differentiation formula, which is up to fifth order, so 1 to 5 model calculations are needed per time step. The code of the Dassl library is used. It is suitable for models having derivative causalities and/or algebraic loops. This simulation algorithm has 4 parameters:

Integration Error (required)
Absolute: The absolute integration error, valid for every state variable (default: 1e-5).
Relative: The relative integration error, valid for every state variable (default: 1e-5).
Step Size (not required)
Initial: The step size for the first simulation step (default: 0.1).
Maximum: The maximum size of a simulation step (default: 1).


Undamped models are not simulated properly with this method.
The default values are suitable for problems with time constants of order of magnitude of 0.1 to 1. Initial Step Size and Maximal Step Size influence the behavior of the method and should be tuned with care.