Back in time. fast. Accelerated time iterations

We present two complementary algorithms to solve nonlinear rational expectations models characterized by first order conditions: an accelerated time-iteration method and a Newton–Krylov solver. Both approaches exploit an explicit construction of the derivative operator (and the model Jacobian) and achieve quadratic convergence near the solution, yielding large computational gains over standard time iteration. We show how to apply these linear operators without forming dense matrices and invert the resulting systems efficiently using truncated Neumann series or GMRES. On three benchmark models (consumption–savings, RBC, and a two-country model), the two methods produce the same solution with substantially reduced runtimes.