Hi everyone,
I am just trying to understand the bigger picture how Dynare solves DSGE models and then checks for the uniqueness of the equilibrium.
Having read this Dynare article, is my following understanding correct:

Dynare makes use of the implicit function theorem (derivatives) and computes the approximation of the policy functions via a Taylor series expansion. The Blanchard Kahn (BK) conditions are then checked/verified via the structural state space of the nonstatic endogenous variables. Is this correct?

At first order, and due to certainty equivalence, instead of using a perturbation approach I could have linearized the model and written it into a state space form and then performed the necessary decompositions to obtain the solution of the model. From there we can check the the BK conditions. Hence, at first order, both approaches should yield the same outcome, correct?

My last question is, when we input the linearized model equations and solve the model with
order = 1
, wouldn’t we doing the same thing twice, i.e. linearizing already linearized equations?
Many thanks for your help.
Best
Robert