Record link: 
http://hdl.handle.net/20.500.12708/199894
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Title: 
A Gauss-Newton continuation method for parameter-dependent boundary value problems using bvpsuite 2.0
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Citation: 
Auzinger, W., Burdeos, K. N., Fallahpour, M., Koch, O., Mendoza, R., & Weinmüller, E. (2024). A Gauss-Newton continuation method for parameter-dependent boundary value problems using bvpsuite 2.0. In International Conference of Numerical Analysis and Applied Mathematics: ICAAM2022 (p. 220009). https://doi.org/10.1063/5.0210220
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Publisher DOI: 
10.1063/5.0210220
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Auzinger, Winfried 
Burdeos, Katrina N. 
Fallahpour, Merlin 
Koch, Othmar 
Mendoza, Renier 
Weinmüller, Ewa 
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Organisational Unit: 
E101 - Institut für Analysis und Scientific Computing 
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Published in: 
International Conference of Numerical Analysis and Applied Mathematics: ICAAM2022 
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ISBN: 
9780735449541
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Volume: 
3094
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Date (published): 
7-Jun-2024
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Event name: 
International Conference of Numerical Analysis and Applied Mathematics (ICNAAM2022) 
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Event date: 
19-Sep-2022 - 25-Sep-2022
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Event place: 
Heraklion, Greece
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Keywords: 
boundary value problems
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Abstract: 
We present a numerical continuation method for the solution of boundary value problems (BVPs) in ordinary differential equations which depends on a free parameter. This method incorporates the open-source bvpsuite 2.0 package [1] for MATLAB in a Gauss-Newton continuation method [2]. The bvpsuite 2.0 package utilizes polynomial collocation [3] equipped with adaptive mesh selection for the solution of boundary value problems. By solving for the free parameter simultaneously with the collocation solution of the BVP, the continuation method is able to cope with turning points in the solution-parameter space. We test our proposed methods on benchmark problems to demonstrate its efficiency.
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Research Areas: 
Mathematical and Algorithmic Foundations: 100%
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Science Branch: 
1010 - Mathematik: 100%
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Appears in Collections:
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