2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70919We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations.For a class of dissipative problems, whose dynamics are characterized by a slow manifold, the Jacobian matrices in such computations are compact perturbations of the identity. We examine the number of GMRES iterations required for each nonlinear iteration as a function of the dimension of the slow subspace and the time-stepper reporting horizon. In a path-following computation, only a small number (one or two) of additional GMRES iterations is required.14 pages, 6 figuresDynamical Systems65F10 (Primary), 65H10 (Secondary), 65H17, 65H20, 65L05text