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Interval length continuation method for solving two-point boundary-value problems

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Abstract

We consider the solution of the following two-point boundary-value problem:

$$\begin{gathered} \dot x(t) = f(t,x(t),p(t)), \dot p(t) = g(t,x(t),p(t)), t \in [0,T], \hfill \\ h(x(0),p(0)) = 0, p(T) = q. \hfill \\ \end{gathered} $$

We propose a combination technique consisting of the interval length continuation method and the back-and-forth shooting method. Certain alternative ways of employing continuation are discussed, and some of them are well suited for the problem under consideration. As a test for the method, a numerical example of a problem originating in optimal control is given.

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References

  1. Orava, P. J., andLautala, P. A. J.,Back-and-Forth Shooting Method for Solving Two-Point Boundary-Value Problems, Journal of Optimization Theory and Applications, Vol. 18, No. 4, 1976.

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Authors and Affiliations

  1. Systems Theory Laboratory, Helsinki University of Technology, Otaniemi, Finland

    P. J. Orava (Teaching and Research Assistant)

  2. Control Engineering Laboratory, Helsinki University of Technology, Otaniemi, Finland

    P. A. J. Lautala (Laboratory Engineer)

Authors
  1. P. J. Orava
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  2. P. A. J. Lautala
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Communicated by S. M. Roberts

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Orava, P.J., Lautala, P.A.J. Interval length continuation method for solving two-point boundary-value problems. J Optim Theory Appl 23, 217–227 (1977). https://doi.org/10.1007/BF00933049

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  • DOI: https://doi.org/10.1007/BF00933049

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