Time-Dependent Reaction Coefficient Identification Problems with a Free Boundary

The determination of time-dependent reaction coefficients in free boundary heat transfer problems is numerically investigated. The additional data which provides a unique solution is given by the Stefan boundary condition and the heat moments. The finite difference method with the Crank-Nicolson scheme combined with a regularized nonlinear optimization is employed. The resulting nonlinear system of equations is solved numerically using the MATLAB toolbox routine lsqnonlin for minimizing the Tikhonov regularization functional. A discussion of the choice of regularization parameters is provided. Numerical results are presented and discussed.