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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R. Bulirsch, J. Stoer, Introduction to Numerical Analysis. Texts in Applied Mathematics, vol. 12, 3rd edn. (Springer, Berlin, 2002)
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, 2015
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)
R.M.M. Mattheij, The conditioning of linear boundary value problems. SIAM J. Numer. Anal. 19(5), 963–978 (1982)
R.M.M. Mattheij, G.W.M. Staarink, On optimal shooting intervals. Math. Comput. 42(165), 25–40 (1984)
Acknowledgements
T.C. was supported by the Deutsche Forschungsgemeinschaft (DFG) through the project CA 633/2-1.
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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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DOI: https://doi.org/10.1007/978-3-319-96415-7_90
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