Variable Step Numerical Schemes on Approximate Inertial Manifolds

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9302938 Chronopoulos This project will study the performance of numerical schemes which combine approximate inertial manifolds with variable step numerical integration. Special emphasis will be given to manifolds which are defined only implicitly, and which result in systems of differential algebraic equations. This research is expected to lead to stable and efficient computational methods for determining the long-time behavior of solutions to certain dissipative nonlinear partial differential equations. Application will be made to the Kuramoto-Sivashinsky and 2-D Navier-Stokes equations. ***