Stability Analysis of Large Time-Stepping Methods for Epitaxial Growth Models

Numerical methods for solving the continuum model of the dynamics of the molecularbeam epitaxy (MBE) require very large time simulation, and therefore large time steps become necessary. The main purpose of this work is to construct and analyze highly stable time discretizations which allow much larger time step than that for a standard implicitexplicit approach. To this end, an extra term, which is consistent with the order of the time discretization, is added to stabilize the numerical schemes. Then the stability properties of the resulting schemes are established rigorously. Numerical experiments are carried out to support the theoretical claims. The proposed methods are also applied to simulate the MBE models with large solution times. The power laws for the coarsening process are obtained and are compared with previously published results. The research of the first author was partially supported by National NSF of China under Grant 10171084 and the Excellent Young Teachers Program by the Ministry of Education of China. The research of this author was supported in part by Hong Kong Research Grants Council and the International Research Team on Complex System of Chinese Academy of Sciences.