Abstract
An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical systems. A quasi-interpolation method due to Hering-Bertram et al. is used to decrease the number of points needed to compute a portion of the manifold. Bézier triangular patches are used in this construction, together with adaptivity conditions based on properties of these patches. Several numerical tests are performed, which show the method to compare favorably with previous approaches.
Original language | English (US) |
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Pages (from-to) | 1734-1745 |
Number of pages | 12 |
Journal | Communications in Nonlinear Science and Numerical Simulation |
Volume | 18 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2013 |
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modeling and Simulation
- Applied Mathematics
Keywords
- Computer-aided geometric design
- Invariant manifold
- Numerical algorithm