An adaptive sequential method is presented for solving the one-dimensional inverse heat conduction problem. The step size, order of parameterization, and amount of the step retained are variable and chosen automatically for each sequence such that optimal, stable results are obtained. A statistical analysis accounting for the stochastic error contributions from both the measured and initial temperatures is derived. Results from the statistical analysis are used to predict stability or instability for a given selection of parameters controlling the inverse method. Simulated experimental applications using inexact data illustrate the practicality of the approach and the effectiveness of the automatic control criteria.

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