A second-order linearized three-level backward Euler scheme for a class of nonlinear expitaxial growth model

Abstract

This article is devoted to the study of the second-order backward Euler scheme for a class of nonlinear expitaxial growth model. The difference scheme is three-level and can achieve second-order convergency in time and space. The unique solvability, unconditional stability and convergency in discrete $L_2$-norm are strictly proved. Numerical examples are also given to validate the theoretical results.

Keywords:

• nonlinear expitaxial growth model
• finite difference
• convergence
• stability

2010 AMS Subject Classifications::

• 65M06
• 65M12
• 65M15

Acknowledgments

Authors thank Dr Zhengru Zhang for helpful discussions. This work is supported by the National Natural Science Foundation of China (Grant No. 11271068, 11326225); Postdoctoral Science Foundation of China (Grant No. 2014M551483); Natural Science Youth Foundation of Jiangsu Province, China (Grant No. BK20130860); and Scientific Research Foundation of Nanjing University of Posts and Telecommunications, China (No. NY213051).