On an approximate method for solving the inverse problem of heat transfer - Il'ya V. Boykov; Vladimir A. Ryazantsev (Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2023)
Background. Developing exact and stable algorithms for solution of inverse problems of mathematical physics is at the leading edge of modern numerical mathematics thanks to rapidly increasing number of applications of such problems in physical and technical sciences as well as some properties of such problems that significantly complicate their solution. In this problem we consider numerical solution of one of such problems that is known as inverse problem of heat conduction. Materials and methods. In this research we use the framework of hypersingular integral equations to develop a numerical method for solution of inverse problem of heat conduction. To the authors’ knowledge, such approach is used to solve this problem for the first time. Results and conclusions. The numerical method described in this paper enables finding approximate solutions of inverse problem of heat conduction including the case of sufficiently big errors in initial data. Solving a model problem shows efficiency of the proposed method.