dc.creator | Li, Shiying | |
dc.date.accessioned | 2020-08-22T17:22:16Z | |
dc.date.available | 2020-07-11 | |
dc.date.issued | 2019-07-11 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-07112019-130042 | |
dc.identifier.uri | http://hdl.handle.net/1803/12932 | |
dc.description.abstract | Splines have been used to approximate the solutions of differential equations for a while. In the first part of this thesis, adaptive algorithms based on the finite element method and splines on triangulations with hanging vertices are introduced and tested. In the second part, spline-based collocation methods are investigated: ordinary collocation, a generalized collocation model in 1D and 2D, and least-squares collocation with splines on triangulations. In particular, existence, uniqueness and error bounds of the (generalized) collocation solutions in the cubic case are presented. An error bound for the least-squares collocation on triangulations in approximating the solutions of the Possion equation is also given. Numerical examples are provided in all of the mentioned cases. | |
dc.format.mimetype | application/pdf | |
dc.subject | Numerical Methods for Differential Equations | |
dc.subject | Collocation Methods | |
dc.subject | Splines | |
dc.subject | Approximation Theory | |
dc.subject | Adaptive Methods | |
dc.title | Adaptive Methods and Collocation by Splines for Solving Differential Equations | |
dc.type | dissertation | |
dc.contributor.committeeMember | Akram Aldroubi | |
dc.contributor.committeeMember | Alexander Powell | |
dc.contributor.committeeMember | Caglar Oskay | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2020-07-11 | |
local.embargo.lift | 2020-07-11 | |
dc.contributor.committeeChair | Larry Schumaker | |
dc.contributor.committeeChair | Marian Neamtu | |