Date of Award:
5-1999
Document Type:
Dissertation
Degree Name:
Doctor of Philosophy (PhD)
Department:
Mathematics and Statistics
Department name when degree awarded
Mathematics
Committee Chair(s)
Joseph Koebbe
Committee
Joseph Koebbe
Committee
Chris Coray
Committee
David Farrelly
Committee
Lance Littlejohn
Committee
Renate Schaaf
Abstract
Numerical schemes for the partial differential equations used to characterize stiffly forced conservation laws are constructed and analyzed. Partial differential equations of this form are found in many physical applications including modeling gas dynamics, fluid flow, and combustion. Many difficulties arise when trying to approximate solutions to stiffly forced conservation laws numerically. Some of these numerical difficulties are investigated.
A new class of numerical schemes is developed to overcome some of these problems. The numerical schemes are constructed using an infinite sequence of conservation laws.
Restrictions are given on the schemes that guarantee they maintain a uniform bound and satisfy an entropy condition. For schemes meeting these criteria, a proof is given of convergence to the correct physical solution of the conservation law.
Numerical examples are presented to illustrate the theoretical results.
Checksum
4d55df8c2da37617af244bcf98db34f8
Recommended Citation
Hillyard, Cinnamon, "Construction and Analysis of a Family of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms" (1999). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7120.
https://digitalcommons.usu.edu/etd/7120
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