Abstract
Surface diffusion is a motion of crystals that the normal velocity of an interface is proportional to the surface Laplacian of mean curvature with respect to the arclength. It is a very popular issue for materials science and applied mathematics. Overview this thesis, our numerical method is based on the finite difference method, compare the numerical results with the results of E. B‥ansch, P. Morin and R. H. Nochetto, which uses the finite element method for surface diffusion, and give the proofs of two known properties of surface diffusion, the preservation of area and the decrease of arclength. Moreover, we also give the sufficient condition for choosing t in our numerical scheme, which makes sure that if t is chosen under the condition, the existence and uniqueness of numerical solution is assured.