AAM  >> Vol. 2 No. 1 (February 2013)

    并行求解抛物型偏微分方程的一种新ASE-I格式
    A New ASE-I Method for Solving Parabolic Equations

  • 全文下载: PDF(351KB)    PP.15-19   DOI: 10.12677/AAM.2013.21003  
  • 下载量: 1,397  浏览量: 5,526  

作者:  

王 栋:山西师范大学,临汾;
冯 蕾:中国科学院光电研究院,北京

关键词:
抛物型方程差分格式并行算法 Parabolicl Equations; Parallel Algorithm; Difference Scheme

摘要:

通过古典显、隐格式和Saul’yev非对称格式,本文构造了一种并行求解抛物型偏微分方程的一种新的ASE-I格式。这种新的差分格式兼具绝对稳定性和高度并行性,并且分段更加灵活,从而这种新的差分格式应用更加广泛。本文给出这种新的差分格式的数学形式,分析了稳定性并得出了稳定性定理。最后通过数值算例验证了这种新ASE-I格式的稳定性和精确性,数值试验结果和理论分析相符合。

In this paper, I construct a new ASE-I scheme for solving parabolic partial differential equations in parallel through classical explicit-implicit format and the Saul’yev asymmetric formats. This method is absolutely parallel and stable, and the sub-sections are more flexible, so the scheme is more convenient to apply to solve parabolic partial differential equations. In this paper, we list the mathematical form of this finite difference scheme, analyze the stability of the scheme, and verify the stability and accuracy of this scheme through numerical experiments. The results of numerical experiments are consistent with the theoretical analysis.

文章引用:
王栋, 冯蕾. 并行求解抛物型偏微分方程的一种新ASE-I格式[J]. 应用数学进展, 2013, 2(1): 15-19. http://dx.doi.org/10.12677/AAM.2013.21003

参考文献

[1] D. J. Evans, M. Sahimi. The alternating group explicit iterative method for solving parabolic equations: 2-dimensional problems. International Journal Computer Mathematics, 1988, 24: 311-341.
[2] B.-L. Zhang, W.-Z. Li. AGE methods with variable coefficient for parabolic computing. Parallel Algorithms and Applications, 1995, 5(3/4): 219-228.
[3] J. Dauglas Jr. A survey of numerical methods for parabolic differential equations. Advances in Computer, Vol.2, Cambridge: Academic Press, 1961: 1-52.
[4] D. J. Evans, A. R. B. Abdullah. A new method for the solution of parabolic differential equations. International Journal of Computer Mathematics, 1991, 38: 241-255.
[5] R. H. Li, B. Liu. The numerical solutions of partial differential equation (3rd Edition). Beijing: Higher Education Press. 2009:107-149. (In Chinese)
[6] D. J. Evans, A. R B. Aboullah. Group explicit methods for parabolic equations. International Journal of Computer Mathematics, 1983, 14(1): 73-105.
[7] L. S. Kang. H. Y. Quan. The numerical solution method of splitting operate for high-dimensional partial differential equation. Shanghai: Shanghai Science and Technology Press, 1990: 1-127.
[8] D. Wang. Operator-splitting methods and its application for solving parabolic equations. Master’s Thesis, Jilin University, 2009. (in Chinese)
[9] D. Y. Li. The Difference Scheme for the solution one-dimensional parabolic equations. Computational Mathematics, 1982, 4(1): 80-90. (in Chinese)