We examine the inverse problem of locating and describing an internal point defect in a one-dimensional rod $\Omega$ by controlling the heat inputs and measuring the subsequent temperatures at the boundary of $\Omega$. We use a variation of the forward heat equation to model heat flow through $\Omega$, then propose algorithms for locating an internal defect and quantifying the effect the defect has on the heat flow. We implement these algorithms, analyze the stability of the procedures, and provide several computational examples.
Kurt Bryan - Department of Mathematics, Rose-Hulman Institute ofTechnology, Terre Haute, IN email@example.com
Gangi, Cynthia and Shah, Sameer
"Characterizing a Defect in a One-Dimensional Bar,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 4
, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol4/iss1/5