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

doi:10.1016/S0252-9602(09)60071-0

Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (4): 803-816.doi: 10.1016/S0252-9602(09)60071-0

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

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

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)

Abstract

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

CLC Number:

65N30

LIU Ti-Wu, XIE Zi-Qing, CHEN Chuan-Miao. THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs[J].Acta mathematica scientia,Series B, 2009, 29(4): 803-816.

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

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