SPECTRAL COLLOCATION METHODS FOR ONE-DIMENSIONAL PHASE-CHANGE PROBLEMS

Single and multi-domain spectral collocation methods utilizing Chebyshev polynomials were employed to obtain highly accurate solutions to one-dimensional phase-change problems. The Landau transformation was imposed to fix the position of the moving boundary. Spatial derivatives were approximated using both spectral and finite-difference representations. Solutions to the resulting ordinary differential equations in time were obtained using the Gear and Adams predictor-corrector algorithms as implemented within the Mathematica programming environment. For test problems in which exact solutions are available, results for the spectral representations compared favorably with solutions obtained using second-order accurate finite-difference approximations.