Publication Cover
Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 9
241
Views
3
CrossRef citations to date
0
Altmetric
Articles

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

, &
Pages 1964-1975 | Received 02 Apr 2014, Accepted 26 Aug 2014, Published online: 10 Oct 2014

References

  • Fujimura H, Yagi A. Homogeneous stationary solution for BCF model describing crystal surface growth. Sci. Math. Jpn. 2009;69:295–302.
  • Grasselli M, Mola G, Yagi A. On the longtime behavior of solutions to a model for epitaxial growth. Osaka J. Math. 2011;48:987–1004.
  • Hunt AW, Orme C, Williams DRM, Orr BG, Sander LM. Instabilities in MBE growth. Europhys. Lett. 1994;27:611–616.
  • Johnson MD, Orme C, Hunt AW, Graff D, Sudijion J, Sauder LM, Orr BG. Stable and unstable growth in molecular beam epitaxy. Phys. Rev. Lett. 1994;72:116–119.
  • Zhao XP, Liu CC. Global attractor for a nonlinear model with periodic boundary value condition. Port. Math. 2012;69:221–231.
  • Zhao XP, Liu FN, Liu B. Finite element method for a nonlinear differential equation describing crystal surface growth. Math. Model. Anal. 2014;19:155–168.
  • Rost M, Krug J. Coarsening of surface structures in unstable epitaxial growth. Phys. Rev. E. 1997;55:3952–3957.
  • Akrivis GD. Finite difference discretization of the Kuramoto-Sivashinsky equation. Numer. Math. 1992;63:1–11.
  • Khiari N, Achouri T, Ben ML. Mohamed, K. Omrani, Finite difference approximate solutions for the Cahn-Hilliard equation. Numer. Methods Partial Differ. Equ. 2007;23:437–455.
  • Khiari N, Omrani K. Finite difference discretization of the extended Fisher-Kolmogorov equation in two dimensions. Comp. Math. Appl. 2011;62:4151–4160.
  • Sun ZZ. A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation. Math. Comput. 1995;64:1463–1471.
  • Choo SM, Chung SK. A conservative nonlinear difference scheme for the viscous Cahn-Hilliard equation. J. Appl. Math. Comp. 2004;16:53–68.
  • Baker GA, Dogalis VA, Karakashian OA. Convergence of Galerkin approximations for the Korteweg-de Vries equation. Math. Comput. 1983;40:419–433.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.