An update strategy for numerically solving boundary value problems

Rideout, M. E. (2009). An update strategy for numerically solving boundary value problems. https://scholar.acadiau.ca/islandora/object/theses:638

Title: An update strategy for numerically solving boundary value problems
Author: Rideout, Matthew Eric
Call Number: LE3 .A278 2009
Date: 2009
Supervisor: Haynes, Ronald
Degree Grantor: Acadia University
Degree Name: Bachelor of Science
Degree Level: Honours
Discipline: Mathematics and Statistics
Affiliation: Mathematics & Statistics
Abstract: Certain types of boundary value problems have solutions which exhibit special properties making it difficult to approximate numerically. The solutions on these regions have rapidly changing features. We explore a method of arriving at an approximation to the solution by choosing a mesh of points across the domain and estimating the value of the solution at those points. One then chooses where it would be beneficial to place additional mesh points along the domain to achieve a better approximation. In this thesis we develop a method to identify the regions requiring a more refined mesh. We then use the Sherman-Morrison-Woodbury formula and the Block Matrix Inverse formula to continually update our approximation to the solution until a user-defined error tolerance has been achieved across the whole domain.
Rights: The author retains copyright in this thesis. Any substantial copying or any other actions that exceed fair dealing or other exceptions in the Copyright Act require the permission of the author.
Permanent Link: https://scholar.acadiau.ca/islandora/object/theses:638

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