计算立方体上Henon方程多个正解的分歧方法

doi:10.12286/jssx.2012.2.113

计算数学 ›› 2012, Vol. 34 ›› Issue (2): 113-124.DOI: 10.12286/jssx.2012.2.113

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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. 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).

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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 Zhaoxiang^1,2, Yang Zhonghua^1,2

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.

关键词： Henon方程, 对称破缺分歧, 多解, 扩张系统, 解枝转接

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.

Key words: Henon equation, symmetry-breaking bifurcation, multiple solutions, extended system, branch switching

MR(2010)主题分类:

35J65
85A15

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摘要

计算立方体上Henon方程多个正解的分歧方法

COMPUTING MULTIPLE SOLUTIONS TO THE BOUNDARY VALUE PROBLEM OF HENON EQUATION

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