Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous computation of trajectories and Poincaré maps

Piotr Zgliczynski
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Submission date: 21. Apr. 2005
Pages: 68
MSC-Numbers: 35B40, 35B45, 65G30, 65N30
Keywords and phrases: periodic orbits, dissipative pdes, galerkin projection, rigorous numerics
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Abstract:
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.