Braga, G. A.Furtado, FredMoreira, J. M.Rolla, L. T.2024-02-082024-02-082003-01-01https://wyoscholar.uwyo.edu/handle/internal/1685https://doi.org/10.15786/wyoscholar/9716In 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.enghttps://creativecommons.org/licenses/by/4.0/renormalization grouppartial differential equationsmultiple scale problemsasymptotic behaviorMathematicsjournal contribution10.1137/S1540345902416600