数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (4): 803-816.doi: 10.1016/S0252-9602(09)60071-0

• 论文 • 上一篇    下一篇

THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs

刘跃武,谢资清,陈传淼   

  1. 1.Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal University, Changsha, 410081, China|2.College of Science, Hunan Agricultural University, Changsha 410128, China
  • 收稿日期:2008-12-29 出版日期:2009-07-20 发布日期:2009-07-20
  • 基金资助:

    This reseach was supported by the National Natural Science Foundation of China (10571053, 10871066, 10811120282), Programme for New Century Excellent Talents in University (NCET-06-0712)

THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs

 LIU Ti-Wu, XIE Zi-Qing, CHEN Chuan-Miao   

  1. 1.Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal University, Changsha, 410081, China|2.College of Science, Hunan Agricultural University, Changsha 410128, China
  • Received:2008-12-29 Online:2009-07-20 Published:2009-07-20
  • Supported by:

    This reseach was supported by the National Natural Science Foundation of China (10571053, 10871066, 10811120282), Programme for New Century Excellent Talents in University (NCET-06-0712)

摘要:

In this paper, we propose an accelerated search-extension method (ASEM)based on the interpolated coefficient finite element method, the search-extension method (SEM) and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in 1-D and 2-D cases will show the efficiency of our approach.

关键词: semilinear PDEs, multiple solutions, accelerated search-extension method (ASEM), two-grid method

Abstract:

In this paper, we propose an accelerated search-extension method (ASEM)based on the interpolated coefficient finite element method, the search-extension method (SEM) and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in 1-D and 2-D cases will show the efficiency of our approach.

Key words: semilinear PDEs, multiple solutions, accelerated search-extension method (ASEM), two-grid method

中图分类号: 

  • 65N30