Numerical Analysis Seminars: Global Stability and Convergence of Timestepping Schemes
13 May 2011 14:15 in E102
When applied to non-trivial dynamical systems,
any timestepping scheme produces a numerical solution
that diverges (almost surely) from the true solution as
$t\to\infty$. Not all is lost, however. In this talk,
we discuss the application of some numerical schemes to
a class of infinite-dimensional dissipative dynamical
systems. By proving global stability in a "strong"
topology, we show that any invariant measure of the
numerical attractor converges to one of the true
attractor's. Potential applications are, eg, turbulence
and climate dynamics.
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