1Division of Integrated BioDefense ISIS Center, Georgetown University Washington, DC 20057, U.S.A Email:
2Aerospace and Mechanical Engineering, Civil Engineering, Mathematics, Systems Architecture Engineering, and Information and Operations Management University of Southern California Los Angeles, CA 900891453, U.S.A.
3Department of Mathematics University of Southern California Los Angeles, CA 90089, U.S.A.
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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 nonpolynomial nonlinearity to show comparison of accuracy for our perturbation method with other wellknown nonlinear Galerkin methods such as FoiasManleyTemam 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.
