Torcont is a software package for the computation and continuation of quasiperiodic invariant tori. A full description and examples of use can be found in the torcont user manual, the theoretical background is explained in the paper Continuation of quasi-periodic invariant tori.
This continuation package consists of finder and continuer programs. It contains algorithms for computation (finder) and continuation (continuer) of
- fixed points (fpfind, fpcont),
- periodic solutions of autonomous and periodically forced systems (pofind, pocont) and
- quasiperiodic solutions of autonomous and periodically forced systems (torfind, torcont; torfind4, torcont4).
The programs use pseudo-arclength continuation. pofind, pocont, torfind and torcont use a finite difference method of order 4. For torfind and torcont, the error is estimated as the difference of solutions obtained by methods of order 2 and 4. The error is largely overestimated, because it is in fact an estimation for the solution of order 2.
torfind4 and torcont4 use a finite element method of order 1. There is no error estimation implemented yet. This programs give much nicer results than torfind and torcont, which is due to the fact, that the FEM does not rely on much smoothness. If you want to use the FEM within Maple, change the procedures torfind and torcont in contpack.mws accordingly, and execute contpack.mws for updating the library contpack.m.
All algorithms are still experimental and not adaptive yet.
| Keywords | Continuation |
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| Contact Person | Frank Schilder, Department of Engineering Mathematics, University of Bristol, [email protected] |
| References to Papers | Frank Schilder: Torcont v1 (2003) User Manual, Applied Nonlinear Mathematics Preprint 2004.18, University of Bristol, 2004.
Frank Schilder, Hinke M. Osinga, Werner Vogt: Continuation of quasi-periodic invariant tori, Applied Nonlinear Mathematics Preprint 2004.11, University of Bristol, 2004. |