Masters Theses

Keywords and Phrases

Difference quotients; proper orthogonal decomposition; reduced order modeling; wave equation


"Recently, researchers have investigated the relationship between proper orthogonal decomposition (POD), difference quotients (DQs), and pointwise in time error bounds for POD reduced order models of partial differential equations. In \cite {Sarahs}, a new approach to POD with DQs was developed that is more computationally efficient than the standard DQ POD approach and it also retains the guaranteed pointwise in time error bounds of the standard method. In this thesis, we extend the new DQ POD approach from \cite {Sarahs} to the case of second difference quotients (DDQs). Specifically, a new POD method utilizing DDQs and only one snapshot and one DQ is developed and used to prove ROM error bounds for the damped wave equation. This new approach eliminates data redundancy in the standard DDQ POD approach that uses all of the snapshots, DQs, and DDQs. We show that this new DDQ approach also has pointwise in time data error bounds similar to DQ POD and use it to prove pointwise and energy ROM error bounds. We provide numerical results and plots for the POD errors and ROM errors to demonstrate the theoretical results. We also explore an application of POD to simulating ROMs past the training interval for collecting the snapshot data for the standard POD approach and the DDQ POD method"-- Abstract, p. iii


Singler, John R.

Committee Member(s)

Grow, David E.
He, Xiaoming


Mathematics and Statistics

Degree Name

M.S. in Applied Mathematics


Missouri University of Science and Technology

Publication Date

Spring 2024


viii, 51 pages

Note about bibliography

Includes_bibliographical_references_(pages 48-50)


© 2023 Andrew Calvin Janes, All rights reserved

Document Type

Thesis - Open Access

File Type




Thesis Number

T 12235

Electronic OCLC #