RESIDUAL-MINIMIZATION LEAST-SQUARES METHOD FOR INVERSE HEAT-CONDUCTION

A numerical method is systematically developed for resolving an invers e heat conduction problem in the presence of noisy discrete data. This paper illustrates the effect of imposing constraints on the unknown f unction of interest. A Volterra integral equation of the first kind is derived and used as the starting point for residual-minimization, lea st-squares methodology. Symbolic manipulation is exploited for purpose s of augmenting the computational methodology. Preliminary indications suggest that the imposition of physical constraints on the system dra stically reduces the level of mathematical sophistication needed for a ccurately approximating the unknown function of interest. These constr aints are actually available in many design studies or from models whi ch are derived by physical processes.