  Bradley et. al. recently provided an explanation of nanodot and defect-free
ordered ripple production from binary compounds, for normal and oblique
incidence ion sputtering respectively, by the inclusion of the effect of the
preferential sputtering of one type of atom relative to the other type on the
surfaces of binary compounds. In this paper, we propose an extended anisotropic
model of such surfaces of type AxB1-x that addresses anisotropy in the
variations of the specie-composition as well. We show that this model gives the
anisotropic Cuerno-Barabasi model as x approaches unity, and analyze the
general properties of the model. Further, the complexity of the solutions of
non-linear higher-order differential equations in general has led to the
creation of great number of highly technical and computationally intensive
numerical schemes. We introduce a simple conformal map method which allows for
a fast and accurate simulation of the dynamical evolution of ion-sputtered
surfaces based on any stochastic continuum model. An optimization algorithm for
an efficient application of the scheme is also introduced. In this scheme the
noise term has a physical meaning which allows one to go beyond the usual white
noise approximation by actually being able to assign physical parameters to it.
