Abstract
In this work,we investigate the inverse problem in the heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We show that this problem can be converted into the first Fredholm integral equation, and an algorithm of inversion is given using the Tikhonov's regularization method. The Newton root-finding algorithm for obtaining the regularization parameter is presented. We also present numerical computations that verify the accuracy of our approximation.
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