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单参数非线性问题中高阶奇异点的计算 被引量:1

Computation of Higher Order Singular Points in Nonlinear Problems with Single Parameter
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摘要 本文考虑计算单参数非线性问题中高阶奇异点的数值方法,基于确定奇异点的一个普适的扩张系统,结合同伦参数的拟弧长延拓,给出了计算各类高阶奇异点的一个统一算法,数值例子表明了算法的有效性. A numerical method for computing the higher order singular points of the nonlinear problems with single parameter. Based on the uniformly extended system and pseudo-arclength continua-tion,an uniform algorithm is given. Numerical examples are computed to show the effectiveness of our algorithm.
出处 《应用数学与计算数学学报》 2003年第2期1-6,共6页 Communication on Applied Mathematics and Computation
基金 上海市科委重点项目 上海市教委重点学科基金资助.
关键词 高阶奇异点 普适扩张系统 拟弧长延拓 同伦参数 正则扩张系统 Higher order singular points,uniformly extended system, pseudo-arclength con-tinuation.
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参考文献5

  • 1Keller, H.B., Numerical solutions of bifurcation and nonlinear eigenvalue problem,In Application of Bifurcation Theory(ed. by P.H. Rabinowitz), Academic Press, New York 1977, 359-384.
  • 2Keller, H.B., Lectures on Numerical Methods in Bifurcation Problems. Springer Verlag, New York 1987.
  • 3Yang Zhonghua, Keller, H.B., A direct method for computing higher order folds, SIAM J. Sci.Stat. Computing, 1986,7: 351-361.
  • 4Yang Zhonghua, Higher order folds in nonlinear problems with several parameters, JCM., 1989,7: 262-278.
  • 5Yang Zhonghua, Classification of pitchfork bifurcation and their computation, Science in China(Series A),1989,32: 537-549.

同被引文献7

  • 1熊波,魏军强,杨忠华.发育生物学中一类反应扩散方程组的分歧分析[J].上海师范大学学报(自然科学版),2003,32(4):28-34. 被引量:1
  • 2Li Changpin,Chen Guorong. Bifurcation Analysis of the Kuramato-Sivashinsky Equation in One Spatial Dimension[J]. Internation Journal of Bifiurcation and Chaos ,2001,9(2) :2493-2499.
  • 3Guckenheimer J, Holmes P. Nonlinear Oscillation Dynamical Systems and Bifurcation of Vector Fields [M]. New York: Springer-Verlag, 1983.
  • 4Yang Zhonghua. Higher Order Folds in Nonlinear Problems with Several Parameters [J]. Journal of Computational Mathematics, 1989,7 : 262-278.
  • 5Yang Zhonghua. Classification of Pitchfork Bifurcation and Their Computation[J]. Science in China Series A, 1989,32: 537-549.
  • 6Yang Zhonghua, Keller H B. A Direct Method for Computing Higher Order Folds[J]. SIAM J Sci Slat Computing, 1986,7:351- 361.
  • 7杨忠华,郭谦.计算二维零空间的非线性分歧问题的新途径[J].高等学校计算数学学报,2000,22(3):279-287. 被引量:1

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