A Handout and some lecture notes.

For a discussion of these methods, see Judd's textbook and also:

Schmitt-Grohe and Uribe, Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function.

Jinill Kim, Sunghyun Kim, Ernst Schaumberg, and Christopher Sims, Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models.

Eric Swanson, Gary Anderson, and Andrew Levin, Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Models.