Rigorous numerics for dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs

Piotr Zgliczyński

Abstract


We describe a Lohner-type algorithm for rigorous integration
of dissipative PDEs. Using it for the Kuramoto-Sivashinsky PDE
on the line with odd and periodic boundary conditions
we give a computer assisted proof the existence of
multiple periodic orbits.

Keywords


Periodic orbits; dissipative PDEs; Galerkin projection; rigorous numerics; computer assisted proof

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