Spherulitic crystallization presents an inverse Stefan problem, which is solved by numerical methods using the DuFort-Frankel scheme and Lagrangian coordinate systems. The numerical solution shows excellent agreement with the analytical solution in the Cartesian coordinate system. A systematic error in the numerical solution for the spherical and cylindrical coordinate systems is examined by a material balance for the system. The systematic error was found to decrease rapidly as the dimensionless time increased and the grid spacing decreased.