A sequential and global method of solving an inverse problem of heat conduction equation

The paper presents a solution to an inverse problem based on the analytical form of the direct problem solution in the convolutional form. The analytical form $ T(r,t)$ is a surface that is fitted to temperature patterns measured (and charged with errors) at the internal points. In the case of quickly-varying patterns, the solution to the inverse problem is highly sensitive to measurement errors (short sampling times). In order to obtain reliable results, the method of sequential (step by step) and global solving of the inverse problem was used together with smoothing the measurement results with the help of hyperbolic spline functions. The numerical results confirm effectiveness of the methods presented in the paper.