SDAE Problems
Mathematical Specification of a Stochastic Differential-Algebraic Equation (SDAE) Problem
To define an SDAE, you simply define an SDE Problem with the forcing function f
, the noise function g
, a mass matrix M
and the initial condition u₀
which define the SDAE in mass matrix form:
f
and g
should be specified as f(u,p,t)
and g(u,p,t)
respectively, and u₀
should be an AbstractArray whose geometry matches the desired geometry of u
. Note that we are not limited to numbers or vectors for u₀
; one is allowed to provide u₀
as arbitrary matrices / higher dimension tensors as well. A vector of g
s can also be defined to determine an SDE of higher Ito dimension.
Nonsingular mass matrices correspond to constraint equations and thus a stochastic DAE.