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Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous computation of trajectories and Poincaré maps
We describe a Lohner-type algorithm for rigorous computation of dissipative PDEs with periodic boundary conditions. The algorithm have been implemented for the Kuramoto-Sivashinsky PDE with odd and periodic boundary conditions and was used to prove the existence of multiple periodic orbits, both stable and unstable ones.