Transformation to ODE System

This section provides utility functions to transform DAE to ODE systems. In particular,

to find equations that need to be differentiated, in order to transform a Differential Algebraic Equations (DAEs) agebraically to Ordinary Differential Equations (ODEs),

to differentiate relevant equations analytically,

Main Functions

ModiaBase.BLTandPantelides.pantelides! — Function

function pantelides!(G, M, A)

Perform index reduction with Pantelides algorithm.

G: bipartite graph (updated)
M: number of V-nodes
A: A[j] = if V[k] = der(V[j]) then k else 0
return assign: assign[j] contains the E-node to which V-node j is assigned or 0 if V-node j not assigned
return A: A[j] = if V[k] = der(V[j]) then k else 0
return B: B[i] = if E[l] = der(E[i]) then l else 0

Reference: Pantelides, C.: The consistent initialization of differential-algebraic systems. SIAM Journal of Scientific and Statistical Computing, 9(2), pp. 213–231 (1988).

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ModiaBase.Differentiate.derivative — Function

der = derivative(ex, timeInvariants=[])

Form the derivative of the expressions ex with regards to time. Time derivative of variables are denoted der(v).

ex: Expression to differentiate
timeInvariants: Vector of time invariant variables, i.e. with time derivative equal to zero.
returnder`: Time derivative of ex

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