Methods for dimension reduction and their application in nonlinear dynamics

We compare linear and nonlinear Galerkin methods in their efficiency to red uce infinite dimensional systems, described by partial differential equatio ns, to low dimensional systems of ordinary differential equations, both con cerning the effort in their application and the accuracy of the resulting r educed system. Important questions like the choice of the form of the ansatz functions (mo des), the choice of the number m of modes and, finally, the construction of the reduced system are addressed. For the latter point, both the linear or standard Galerkin method making use of the Karhunen Loeve (proper orthogon al decomposition) ansatz functions and the nonlinear Galerkin method, using approximate inertial manifold theory, are used. In addition, also the post -processing Galerkin method is compared with the other approaches. (C) 2001 Elsevier Science Ltd. All rights reserved.