Advertisement

Applied Mathematics and Mechanics

, Volume 14, Issue 3, pp 235–239 | Cite as

Four-point explicit difference schemes for the dispersive equation

Article

Abstract

A class of three-level explicit difference schemes for the dispersive equation u1=auzzz are established. These schemes have higher stability and involve four mesh points at the middle level. Their local truncation errors are O(τ+h) and stability conditions are from |R|≤0.25 to |R|≤10, where |R|=|a|τ/h3, which, is much better than |R|≤0.25[1].

Key words

dispersive equation four-point explicit difference scheme higher stability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Qin Meng-zhao, The difference schemes of the dispersive equation ut=auzzz,Mathematica Numerical Sinica,6, 1 (1984), 1–13.Google Scholar
  2. [2]
    Wu Hua-mo, A class of three-level explicit schemesH with higher stability properties for dispersion equations,Mathematica Numerica Sinica 8, 3 (1986), 329–331.MathSciNetGoogle Scholar
  3. [3]
    Wu Hua-mo, Elementary proof of the Schur-Cohn-Miller theorem.Journal on Numerical Methods and Computer Applications,2, 2 (1982), 63–64.Google Scholar
  4. [4]
    Liu Peng-cheng, A class of three-level explicit schemes with higher stability properties for a dispersive equation ut=auzzz Applied Mathematics and Mechanics,9, 9 (1988), 803–808.MathSciNetGoogle Scholar
  5. [5]
    Dai Jia-zun, Zhao Ning and Xu Yun, On a class of explicit difference schemes for the dispersive equation u1=auzzz Mathematica Numerica Sinica,11, 2 (1989), 172–177.Google Scholar
  6. [6]
    Dai Wei-zhong, Stable explicit and semi-explicit three-level difference schemes for the dispersive equation ut=auzzz Journal of Xiamen University (Natural, Science),27, 1 (1988), 116–118. (in Chinese)Google Scholar
  7. [7]
    Li Yi and Li Bei-jie, Two explicit difference schemes for the dispersive equation ut=auzzz Mathematica Numerica Sinica,8, 3 (1986), 275–280.MathSciNetGoogle Scholar
  8. [8]
    Li Yi, Three-level explicit difference schemes for the dispersion equation ut=auzzz Journal of Sichuan University (Natural Science Edition),25, 3 (1988), 298–306. (in Chinese)MathSciNetGoogle Scholar
  9. [9]
    Li Yi and Wu Wei-wen, Explicit difference schemes for the dispersion equation,Journal of Chongqing University, 3 (1990). (in Chinese)Google Scholar
  10. [10]
    Richtmyer, R. D. and K. W. Morton,Difference Methods for Initial-Value Problems, John Wiley and Sons (1967), 68–90.Google Scholar
  11. [11]
    Li Yi. A class of three-level explicit difference scheme (to appear)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1993

Authors and Affiliations

  • Li Yi
    • 1
  1. 1.Department of MathematicsSichuan UniversityChengdu

Personalised recommendations