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Extension of a perturbation technique for nonlinear two-point boundary-value problems

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Abstract

This paper extends the perturbation method of Roberts and Shipman by introducing the concept of a general partitioning scheme. Three specific realizations of the general partitioning idea (linear, variational, and quasilinear partitions) are described with supporting numerical results. To date, numerical experience with these methods indicates that the quasilinear partition method is the best.

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References

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Authors and Affiliations

  1. Data Processing Division, IBM, Palo Alto, California

    S. M. Roberts (Advisory Analyst)

  2. Federal Systems Division, IBM, Gaithersburg, Maryland

    J. S. Shipman (Advisory Mathematician)

Authors
  1. S. M. Roberts
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  2. J. S. Shipman
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Additional information

Communicated by R. E. Kalaba

We wish to acknowledge Dr. G. N. Lance, Chief, Division of Computing Research, Commonwealth Scientific and Industrial Research Organization, Canberra City, Australia, who suggested that we develop partition methods beyond those given in Ref. 1.

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Roberts, S.M., Shipman, J.S. Extension of a perturbation technique for nonlinear two-point boundary-value problems. J Optim Theory Appl 12, 459–470 (1973). https://doi.org/10.1007/BF00935241

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