The eigenvalue problem couples the interface and the temperature field, and is solved on an infinite domain. The computed eigenvalue corresponds to the growth rate of the crystal, and the computed eigenvector consists of both the the interface and temperature perturbation. Using a straightforward transformation, we map the parabolic interface of the stationary solution to a horizontal line in an infinite rectangular domain. It is observed from the following picture that the interface becomes more oscillatory as the growth rate increases, which confirms the Mullins-Sekerka instability theory.