Integration Overview

In order to get some scope I have prepared a new diagram where the different integration fields of any multibody physics engine can be fit.
Normally we have to integrate time, via ODEs, for which any of the available schemes can be chosen, but then also the Differential Algebraic Equations for constraints (related to collisions) and the Partial Differential Equations related to the continuum have to be solved.
Of course, not every engine implements the continuum part (limiting to rigid solid) and some matter integration schemes already consider the very collisions so the constraint integration is explicitly sorted...
The associated disciplines where each concept fits are represented by the horizontal blocks.