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Semidiscretisation Methods for Quasi‐periodic Solutions
Author(s) -
Schilder F.,
Vogt W.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310231
Subject(s) - ode , a priori and a posteriori , torus , mathematics , invariant (physics) , ordinary differential equation , mathematical analysis , periodic system , differential equation , geometry , philosophy , epistemology , mathematical physics
The aim of our approach is a reliable numerical approximation of quasi‐periodic solutions of periodically forced ODEs without using a‐priori transformations into new coordinates [1]. The invariant torus is computed as a solution of a special invariance equation. In the case of two basic frequencies this system can be solved by semidiscretisation, which transforms the system into a higher dimensional autonomous ODE system with periodic solutions.
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