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

#### 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.

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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