High-order adaptive methods for computing invariant manifolds of maps

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses Bezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of Bezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the method for parametric surfaces and then he adapts this method to invariant manifolds of three-dimensional maps.

Name thesis:degree_name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Discipline thesis:degree_discipline

Mathematical Sciences

Year

2011

Author dc:creator

• Wrobel, Jacek K.

Contributors dc:contributor

• Roy Goodman
• Denis L. Blackmore
• Amitabha Koshal Bose

• Inconvenient manifold
• Computer-aided geometric design
• Numerical algorithm
• Mathematics

Repository record dc:identifier

https://digitalcommons.njit.edu/dissertations/267

OAI identifier oai:identifier

oai:digitalcommons.njit.edu:dissertations-1322