How does Dynare solve policy functions?

[superztt]

I want to know more how dynare solves policy functions.

Chapter 7.3 in User Guide says, there are a series of algebraic trics to solve the policy functions(gy, gu) after first order Taylor expansion of necessary conditions, detailed in Michel Juillard's presentation. The reference I found in the end of the User Guide is, Juillard, M. (1996): \Dynare : a program for the resolution and simulation
of dynamic models with forward variables through the use of a relaxation algorithm. Is this the one detailing the trics?

If not, where can I find the right answer? If so, I don't see how this paper explains how dynare works. Because seems this paper relies on initial and terminal conditions, while I thought dynare solves time-irrespective models. Thanks!

[jpfeifer]

For stochastic models, Dynare uses standard perturbation techniques. The particular variant used for solving the quadratic matrix equation at first order is not that important, but is documented in Villemot's paper. You can think of it like Blanchard/Kahn, Uhlig, Klein, Sims, or the method of undetermined coefficients. Up to some small numerical error, they will all return the same results

For deterministic/perfect foresight models, Dynare solves the arising nonlinear equation system using a Newton-type method.