ANALYSIS OF SEQUENTIAL METHODS OF SOLVING THE INVERSE HEAT CONDUCTION PROBLEM

Abstract

The emphasis of this article is on an error and stability analysis of sequential methods solving the linear inverse heat conduction problem. The well-known method of J. V. Beck is studied as well as modifications thereof. At the end, our results are discussed by means of numerical examples.

The following aspects are most important in the article. A fundamental relation is established that shows how the heat fluxes determined by Beck's method depend explicitly on the previous heat fluxes and on the data. On the one hand, this presents a new way of computing the Beck method and, on the other hand, leads to various modifications of the method for which analogous relations and computational procedures are available. Moreover, for all sequential methods under consideration, an error analysis can be established.