On an Approximate Method for Solving the Inverse Problem of Heat Transfer

The problems of constructing accurate and stable algorithms for solving inverse problems of mathematical physics are at the forefront of modern computational mathematics due to the ever-increasing number of applications of such problems in physics and technology, as well as to the properties of these problems, which greatly complicate their numerical solution. In this paper, we consider the problem of numerical solution of one of such problems, known as the inverse problem of heat transfer. The numerical method for solving the inverse problem of heat transfer uses the apparatus of hypersingular integral equations. As far as the authors know, this approach to the construction of methods for solving the inverse problem of heat transfer is used for the first time. The numerical method described in the paper makes it possible to successfully find an approximate solution to the inverse problem of heat transfer, including the case of significant errors in the initial data. The solution of a model example demonstrates the efficiency of the method proposed.