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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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