Aspects of Continuation Software

  • W. C. Rheinboldt
  • D. Roose
  • R. Seydel
Part of the NATO ASI Series book series (ASIC, volume 313)

Abstract

In recent years, many continuation algorithms have been implemented. In order to assess the various aspects of these codes, this paper presents a list of features and options that appear to be necessary or desirable for continuation codes. With this it is hoped to provide a framework for writing further such codes, and for judging their differences.

Keywords

Bifurcation Point Step Length Target Point Local Coordinate System Continuation Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1.]
    Allgower, E.L., Schmidt, P.H. (1985) An algorithm for piecewise-linear approximation of an implicitly defined manifold. SI AM J. Numer. Anal. 22, 322–346.MathSciNetMATHCrossRefGoogle Scholar
  2. [2.]
    Bank, R.E. (1988) PLTMG User’s Guide — Edition 5. 0. University of California, La Jolla.Google Scholar
  3. [3.]
    Deufihard, P., Fiedler, B., Kunkel, P. (1987) Efficient numerical path-following beyond critical points. SIAM J.Numer.Anal. 24, 912–927.MathSciNetCrossRefGoogle Scholar
  4. [4.]
    Doedel, E. (1986) AUTO: Software for continuation and bifurcation problems in ordinary differential equations. California Institute of Technology, Pasadena.Google Scholar
  5. [5.]
    Kaas-Peterson, C. (1987) PATH — User’s Guide. University at Leeds, Centre for nonlinear studies.Google Scholar
  6. [6.]
    Morgan, A. (1987) Solving Polynomial Systems Using Continuation. Prentice Hall, Englewood.MATHGoogle Scholar
  7. [7.]
    Rheinboldt, W.C. (1986) Numerical Analysis of Parametrized Nonlinear Equations. J.Wiley, New York.MATHGoogle Scholar
  8. [8.]
    Rheinboldt, W.C. (1988) On the computation of multi-dimensional solution manifolds of parametrized equaitions. Numer.Math. 53, 165–181.MathSciNetMATHCrossRefGoogle Scholar
  9. [9.]
    Rheinboldt, W.C., Burkardt, J. (1983) A locally parametrized continuation process. ACM Transactions of Math. Software 9, 215–235.MathSciNetMATHCrossRefGoogle Scholar
  10. [10.]
    Rosendorf, P., Orsag, J., Schreiber, I., Maxek, M. (1989) Interactive System for Studies in Nonlinear Dynamics. Prague Institute of Chemical Technology, Prague.Google Scholar
  11. [11.]
    Seydel, R. (1988) From Equilibrium to Chaos. Practical Bifurcation and Stability Analysis. Elsevier, New York.Google Scholar
  12. [12.]
    Seydel, R. (1989) BIFPACK, a program package for continuation, bifurcation, and stability analysis. University at Würzburg.Google Scholar
  13. [13.]
    Watson, L.T., Billups, S.C., Morgan, A.P. (1987) HOMPACK: A suite of codes for globally convergent homotopy algorithms. ACM Transactions on Math. Software 13, 281–310.MathSciNetMATHCrossRefGoogle Scholar
  14. [14.]
    Wood, E.F., Kempf, J.A., Mehra, R.K. (1984) BISTAB: A portable bifurcation and stability analysis package. Appl. Math. Comp. 15 (1984) 343–355.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • W. C. Rheinboldt
    • 1
  • D. Roose
    • 2
  • R. Seydel
    • 3
  1. 1.Dept. of Mathematics and StatisticsUniversity of PittsburghPittsburghUSA
  2. 2.Dept. Computer ScienceK.U. LeuvenHeverleeBelgium
  3. 3.Applied MathematicsUniversity at WurzburgWürzburgFed. Rep. Germany

Personalised recommendations