Skip to main content
SpringerLink
Log in

A class of alternating group method of Burgers’ equation

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Some new Saul’ yev type asymmetric difference schemes for Burgers’ equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers’ equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Evans D J, Abdullah A R B. Group explicit methods for parabolic equations[J].Internat J Computer Math, 1983,14(1):73–105.

    MATH  MathSciNet  Google Scholar 

  2. Evans D J. Alternating group explicit method for the diffusion equations[J].Appl Math Modelling, 1985,9(3)201–206.

    Article  MATH  MathSciNet  Google Scholar 

  3. Evans D J, Abdullah A R B. A new explicit method for the diffusion-convection equation[J].Comput Math Appl, 1985,11(1/3):145–154.

    Article  MATH  MathSciNet  Google Scholar 

  4. ZHANG Bao-lin, SU Xiu-min. Alternating block explicit-implicit method for two-dimensional diffusion equation[J].Internat J Computer Math, 1991,38(3/4):241–255.

    Google Scholar 

  5. ZHANG Bao-lin, LI Wen-zhi. On alternating segment Crank-Nicolson scheme[J].Parallel Computing, 1994,20(8):897–902.

    Article  MathSciNet  Google Scholar 

  6. Evans D J, Sahimi M S. The numerical solution of Burgers’ equations by the alternating group explicit (AGE) method[J].Internat J Computer Math, 1989,29(1):39–64.

    MATH  Google Scholar 

  7. Evans D J, Abdullah A R B. The group explicit method for the Burgers’ equations[J].Computing, 1984,32(3):239–252.

    Article  MATH  MathSciNet  Google Scholar 

  8. LU Jin-fu, ZHANG Bao-lin, XU Tao. AGE method for two-dimensional Burgers’ equation and parallel computing[J].Chinese Journal of Computational Physics, 1998,15(2):225–233. (in Chinese)

    Google Scholar 

  9. JIN Cheng-ri, LIU Jia-qi. An alternating group explicit iteration method for Burgers’ equation[J].Chinese Journal of Computational Physics, 1998,15(5):607–613. (in Chinese)

    Google Scholar 

  10. WANG Zi-ding, LU Jin-fu, XIAO Shi-jiang. Group explicit method for Burgers’ equation[J].Chinese Journal of Computational Physics, 1993,10(4):479–487. (in Chinese)

    Google Scholar 

  11. Kellogg R B. An alternating direction method for operator equations[J].J Soc Indust Appl Math (SIAM), 1964,12(4):848–854.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and System Science, Shandong University, 250100, Jinan, P.R. China

    Wang Wen-qia Professor

Authors
  1. Wang Wen-qia Professor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by LI Ji-bin

Foundation item: the Doctorate Foundation of the State Education Department of China (97042202); the Natural Science Foundation of Shandong Province of China (Y2003A04)

Biography: WANG Wen-qia (1950≈)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wen-qia, W. A class of alternating group method of Burgers’ equation. Appl Math Mech 25, 236–244 (2004). https://doi.org/10.1007/BF02437325

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02437325

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation