A difference method for solving inverse heat-conduction problems concerning the determination of the geometric characteristics of a body or a field

The paper develops a difference method for solving inverse geometric problems of heat conduction relating to the determination of the coordinates of a moving boundary with respect to steps along the time axis. At every step, the desired function is expanded in a power series of the time coordinate; and the coefficients of this series are found through the multiple solution of direct heat-conduction problems for systems with moving phase boundaries. Numerical results indicate that the error of the solution of incorrectly stated inverse geometric problems differs only insignificantly from the error of the initial data.