Scaling and renormalization group (RG) methods are used to study
parabolic equations with a small nonlinear term and find the decay
exponents. The determination of decay exponents is viewed as an
asymptotically self similar process that facilitates an RG
approach. These RG methods are extended to higher order in the
small coefficient of the nonlinearity. The RG results are verified
in some cases by rigorous proofs and other calculational methods.