Finite difference discretization of a fourth-order parabolic equation describing crystal surface growth

Abstract

In this paper, by using finite difference method, we consider the approximate solutions for a fourth-order parabolic equation describing crystal surface growth.

Keywords:

• finite difference scheme
• fourth order parabolic equation
• convergence
• error estimate

AMS Subject Classifications:

• 65M06
• 65M15

Acknowledgements

The authors thank the referees for their valuable comments and suggestions about this article.

Notes

This paper is supported by the Natural Science Foundation of China for Young Scholar [grant number 11401258] and Natural Science Foundation of Jiangsu Province of China for Young Scholar [grant number BK20140130].