On a computational approach for the approximate dynamics of averaged   variables in nonlinear ODE systems: toward the derivation of constitutive   laws of the rate type
  A non-perturbative approach to the time-averaging of nonlinear, autonomous ODE systems is developed based on invariant manifold methodology. The method is implemented computationally and applied to model problems arising in the mechanics of solids. 
Amit Acharya and Aarti Sawant