Accuracy of the two-iteration spectral method for phase change problems

The accuracy of the solution of phase change problems using a spectral method is studied. Two iterations in the expansion are used to obtain the interface location of a solidification problem in semi-infinite domain. Asymptotic expansion of the current approach is compared to the existing analytical solution of the problem, and the validity of the expansion is studied. The results indicate the accuracy of a numerical application of the current approach to finite and semi-infinite geometries.