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Abstract

Given an initial-boundary value problem as model of a heated rod of unknown length, we consider the inverse problem of determining this length from temperature and heat flux measurements at one end of the rod. This models the situation where one end of the rod is inaccessible. We derive and test two different algorithms to numerically estimate the length of the rod, and demonstrate their performance through numerical examples.

Author Bio

Nathaniel Givens graduated from the University of Richmond in May 2005with a B.S. in mathematics and a minor in computer science.The researchpresented in this article was conducted with fellow University of Richmondstudents Robin Haskins and Daniel Katz during the summer of 2004. He iscurrently employed as an analyst, and will be continuing his educationinto either statistics or mathematical modeling. His other interestsinclude free-will philosophy, theology, and science fiction.

Robin Haskins is a double major in Mathematics and Computer Science and will be graduating from the University of Richmond in the spring of 2006. The research presented in this paper was performed during the summer of 2004 as a undergraduate research summer fellowship at the University of Richmond.Although Robin does not have specific plans for life after graduation, she plans to one day pursue a Ph.D. in mathematics.

Daniel Katz is currently a senior at the University of Richmond, persuing a B.S. in mathematics, with honors, and interdisciplinary physics. The research presented in this article was conducted with fellow University of Richmond students Robin Haskins and Nathaniel Givens during the summer of 2004. After completing his undergraduate degree in December of 2005, Mr. Katz plans on continuing his education in applied mathematics at the graduate level.

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