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Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous computation of trajectories and Poincaré maps
Piotr ZgliczynskiAbstract
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.
- Received:
- 21.04.05
- Published:
- 21.04.05
- MSC Codes:
- 35B40, 35B45, 65G30, 65N30
- Keywords:
- periodic orbits, dissipative pdes, galerkin projection, rigorous numerics