Modified Backward Differentiation Formula (MBDF)

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Modified Backward Differentiation Formula (MBDF)

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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. The MBDF allows the use of constraint variables when proper initial values are used.


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).


This is the only method that supports the use of the constraint function.
The MeBDFi method cannot handle contraints that do not influence the model. Therefore 20-sim will check at the beginning of the simulation if contraints have been properly defined. The contraints that do not influence the model are set to zero automatically. If you do not want to use this check, deselect the Smart Contraint Solving option.
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.