Time-marching on the slow manifold: The relationship between the nonlinear Galerkin method and implicit timestepping algorithms

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Abstract

Implicit timestepping schemes and the Nonlinear Galerkin (NG) algorithms are competitors for integrating on the slow manifold, that is, for computing solutions when the timestep- limiting high frequencies are physically unimportant and most of the energy is in low frequency flow. We show that implicit schemes are always at least as accurate as the lowest nontrivial NG method, and can be made superior to even high order NG schemes by shortening the time step.

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This work was supported by the NSF ECS9012263, NSF OCE9119459 and DOE KC070101.