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

Chuanju Xu*, Tao Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

268 Citations (Scopus)
36 Downloads (Pure)


Numerical methods for solving the continuum model of the dynamics of the molecular beam 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 steps than those of a standard implicit‐explicit 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.

Original languageEnglish
Pages (from-to)1759-1779
Number of pages21
JournalSIAM Journal on Numerical Analysis
Issue number4
Publication statusPublished - 26 Sept 2006

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Epitaxial growth
  • Implicit-explicit method
  • Large time-stepping
  • Molecular beam epitaxy
  • Spectral method
  • Stability


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