Advertisement

Adaptive Multiple Shooting for Nonlinear Boundary Value Problems

  • Thomas CarraroEmail author
  • Michael Ernst Geiger
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

Multiple shooting methods are time domain decomposition methods suitable for solving boundary value problems (BVP). They are based on a subdivision of the time interval and the integration of appropriate initial value problems on this subdivision. In certain critical cases, systematic adaptive techniques to design a proper time domain decomposition are essential. We extend an adaptive shooting points distribution developed in the 1980s for linear boundary value problems based on ordinary differential equations (ODE) to the nonlinear case.

Notes

Acknowledgements

T.C. was supported by the Deutsche Forschungsgemeinschaft (DFG) through the project CA 633/2-1.

References

  1. 1.
    R. Bulirsch, J. Stoer, Introduction to Numerical Analysis. Texts in Applied Mathematics, vol. 12, 3rd edn. (Springer, Berlin, 2002)Google Scholar
  2. 2.
    M.E. Geiger, Adaptive multiple shooting for boundary value problems and constrained parabolic optimization problems, Ph.D. thesis, Ruprecht-Karls-Universität Heidelberg, Fakultät für Mathematik und Informatik, 2015Google Scholar
  3. 3.
    R.M.M. Mattheij, Estimates for the errors in the solutions of linear boundary value problems, due to perturbations. Computing 27(4), 299–318 (1981)MathSciNetCrossRefGoogle Scholar
  4. 4.
    R.M.M. Mattheij, The conditioning of linear boundary value problems. SIAM J. Numer. Anal. 19(5), 963–978 (1982)MathSciNetCrossRefGoogle Scholar
  5. 5.
    R.M.M. Mattheij, G.W.M. Staarink, On optimal shooting intervals. Math. Comput. 42(165), 25–40 (1984)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Heidelberg UniversityHeidelbergGermany
  2. 2.d-fine GmbHFrankfurt/MainGermany

Personalised recommendations