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.
Lester Caudill, Department of Mathematics and Computer Science, University of Richmond firstname.lastname@example.org
Givens, Nathaniel; Haskins, Robin; and Katz, Daniel
"Estimation of the Length of a Rod from Thermal Data,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 6
, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol6/iss1/5