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MiS Preprint
39/2005

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

Piotr Zgliczynski

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.

Received:
Apr 21, 2005
Published:
Apr 21, 2005
MSC Codes:
35B40, 35B45, 65G30, 65N30
Keywords:
periodic orbits, dissipative pdes, galerkin projection, rigorous numerics

Related publications

Preprint
2005 Repository Open Access
Piotr Zgliczynski

Rigorous numerics for dissipative PDEs III. : an effective algorithm for rigorous computation of trajectories and Poincaré maps