Inertial manifolds under multistep discretization
نویسنده
چکیده
Finite-dimensional inertial manifolds attract solutions to a nonlinear parabolic diierential equation at an exponential rate. In this paper inertial manifolds for multistep discretizations of such equations are studied. We provide an existence result for inertial manifolds under multistep discretization and show that these inertial manifolds converge to the inertial manifold of the original equation with the order of the multistep method. For the existence proof error estimates concerning nonsmooth-data are needed, and these are also given in this paper. Our results are applied to the complex Ginzburg-Landau equation.
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