Method for determining the temperature state of a cylinder at the heat treatment with incomplete initial data

The paper is devoted to the problem of determining the temperature inside the cylinder based on the surface measurements. The main characteristics of the material such as specific heat, thermal conductivity and material density depend on the temperature at each point of the body. This problem appears in complex heat treatment of products. The mathematical model of heat transfer is presented as nonlinear heat conduction equation with unknown initial condition. In this problem, both the Dirichlet and Neumann boundary conditions are given. The computational scheme of the method is based on the using of finite-difference equations and regularization technique. This approach allows to obtain the temperature inside cylindrical body and then to determine the unknown temperature on the cylinder axis. We investigate the stability of computational method and obtain the dependence of stability on the discretization steps and level error of the initial data. The reliability and the efficiency of the method were confirmed by results of computational experiments.