High-order adaptive method for computing two-dimensional invariant manifolds of three-dimensional maps

Jacek K. Wróbel, Roy H. Goodman

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 languageEnglish (US)
Pages (from-to)1734-1745
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume18
Issue number7
DOIs
StatePublished - Jul 2013

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Computer-aided geometric design
  • Invariant manifold
  • Numerical algorithm

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