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计算立方体上Henon方程多个正解的分歧方法

李昭祥1,2, 杨忠华1,2   

  1. 1. 上海师范大学计算数学系, 上海 200234;
    2. 科学计算上海高校重点实验室, 上海 200234
  • 收稿日期:2009-10-08 出版日期:2012-05-15 发布日期:2012-05-20
  • 基金资助:

    国家自然科学基金(批准号:10901106);上海重点学科建设项目(批准号:S30405);上海市自然科学基金(批准号:09ZR1423200);上海市科委创新项目(批准号:09YZ150).

李昭祥, 杨忠华. 计算立方体上Henon方程多个正解的分歧方法[J]. 计算数学, 2012, 34(2): 113-124.

Li Zhaoxiang, Yang Zhonghua. COMPUTING MULTIPLE SOLUTIONS TO THE BOUNDARY VALUE PROBLEM OF HENON EQUATION[J]. Mathematica Numerica Sinica, 2012, 34(2): 113-124.

COMPUTING MULTIPLE SOLUTIONS TO THE BOUNDARY VALUE PROBLEM OF HENON EQUATION

Li Zhaoxiang1,2, Yang Zhonghua1,2   

  1. 1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China;
    2. Scientific Computing Key Laboratory of Shanghai University, Shanghai, 200234, China
  • Received:2009-10-08 Online:2012-05-15 Published:2012-05-20
本文首先应用分歧方法给出计算立方体上Henon方程边值问题D4(3)对称正解的三种算法, 然后以Henon方程中的参数r为分歧参数, 在D4(3)对称正解解枝上 用扩张系统方法求出对称破缺分歧点, 进而用解枝转接方法计算出其它具有不同对称性质的正解.
Three algorithms based on the bifurcation method are applied to computing the D4(3) symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation points are found via the extended systems on the branch of the D4(3) symmetric positive solutions. Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.

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