A Perturbation Approach for Approximate Inertial Manifolds

We present an explicit form for the construction of approximate inertial manifolds (AIMs) for a class of nonlinear dissipative partial differential equations by using a perturbation technique. We investigate two numerical examples of the reaction diffusion equation with polynomial nonlinearity and non-polynomial nonlinearity to show comparison of accuracy for our perturbation method with other well-known nonlinear Galerkin methods such as Foias-Manley-Temam and EulerGalerkin methods. The proposed method for obtaining approximate inertial manifolds, though computationally more expensive, provides superior accuracy when compared with other AIM methods currently in use. 16 D. Kim, F. Udwadia and W. Proskurowski