  In this paper we present an efficient numerical approach based on the
Renormalization Group method for the computation of self-similar dynamics. The
latter arise, for instance, as the long-time asymptotic behavior of solutions
to nonlinear parabolic partial differential equations. We illustrate the
approach with the verification of a conjecture about the long-time behavior of
solutions to a certain class of nonlinear diffusion equations with periodic
coefficients. This conjecture is based on a mixed argument involving ideas from
homogenization theory and the Renormalization Group method. Our numerical
approach provides a detailed picture of the asymptotics, including the
determination of the effective or renormalized diffusion coefficient.
