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Direct Multiple Shooting and Generalized Gauss-Newton Method for Parameter Estimation Problems in ODE Models

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Multiple Shooting and Time Domain Decomposition Methods

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 9))

Abstract

The paper presents a boundary value problem approach for optimization problems in nonlinear ordinary differential equations, in particular for parameter estimation, based on multiple shooting as originally introduced by Bock in the 1970s. A special emphasis is placed on the theoretical analysis including numerical stability, grid condition and a posteriori error analysis. The paper discusses advantages of multiple shooting versus single shooting which are illustrated by numerical examples.

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Author information

Authors and Affiliations

  1. IWR, Heidelberg University, Heidelberg, Germany

    Hans Georg Bock & Johannes P. Schlöder

  2. IAM, Heidelberg University, Heidelberg, Germany

    Ekaterina Kostina

Authors
  1. Hans Georg Bock
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  2. Ekaterina Kostina
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  3. Johannes P. Schlöder
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Corresponding author

Correspondence to Ekaterina Kostina .

Editor information

Editors and Affiliations

  1. Heidelberg University, Institute for Applied Mathematics, Heidelberg, Germany

    Thomas Carraro

  2. Heidelberg University, Institute for Applied Mathematics, Heidelberg, Germany

    Michael Geiger

  3. Heidelberg University, Interdisciplinary Center for Scientific Computing, Heidelberg, Germany

    Stefan Körkel

  4. Heidelberg University, Institute for Applied Mathematics, Heidelberg, Germany

    Rolf Rannacher

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Bock, H.G., Kostina, E., Schlöder, J.P. (2015). Direct Multiple Shooting and Generalized Gauss-Newton Method for Parameter Estimation Problems in ODE Models. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds) Multiple Shooting and Time Domain Decomposition Methods. Contributions in Mathematical and Computational Sciences, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-23321-5_1

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