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Adaptive Multiple Shooting for Nonlinear Boundary Value Problems

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Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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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.

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References

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Acknowledgements

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

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Authors and Affiliations

  1. Heidelberg University, Heidelberg, Germany

    Thomas Carraro & Michael Ernst Geiger

  2. d-fine GmbH, Frankfurt/Main, Germany

    Michael Ernst Geiger

Authors
  1. Thomas Carraro
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  2. Michael Ernst Geiger
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Corresponding author

Correspondence to Thomas Carraro .

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Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Carraro, T., Geiger, M.E. (2019). Adaptive Multiple Shooting for Nonlinear Boundary Value Problems. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_90

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