Many applications in contemporary science involve multiscale dynamics with
time and space scale separation of patterns of motion, with fewer slowly
evolving variables and much larger set of faster evolving variables. A direct
numerical simulation of the evolution of such dynamics is typically
computationally expensive, due to both the large number of fast variables and
necessity for a small discretization time step to resolve fast components of
dynamics.
The recently developed short-time linear response algorithm, which predicts
the average response of a nonlinear chaotic system with forcing and dissipation
to small external perturbation, generally yields high precision of the response
prediction, although suffers from numerical instability for long response times
due to positive Lyapunov exponents.