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A fast accurate artificial boundary condition for the Euler-Bernoulli beam

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Abstract

It is difficult to convert the PDEs defined on the whole space with higher order space derivatives into initial boundary value problems by proposing boundary conditions. In this paper, we use an absorbing boundary condition method to solve the Cauchy problem for one-dimensional Euler-Bernoulli beam with fast convolution boundary condition which is derived through the Padé approximation for the square root function \(\sqrt {\cdot }\). We also introduce a constant damping term to control the error between the resulting approximation of the Euler-Bernoulli system and the original one. Numerical examples verify the theoretical results and demonstrate the performance for the fast numerical method.

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Acknowledgements

The authors thank Prof Xavier Antonine for useful help and suggestions.

Funding

This research is partially supported by NSFC under grant Nos. 11832001 and 11502028.

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Authors and Affiliations

  1. Chongqing University of Technology, Chongqing, 400054, China

    Zijun Zheng

  2. School of Mathematical Science, Beihang University, Beijing, 102206, China

    Gang Pang

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  1. Zijun Zheng
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  2. Gang Pang
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Correspondence to Gang Pang.

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Zheng did the numerical computation. Pang proposed the numerical algorithms and gave the proof.

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Zheng, Z., Pang, G. A fast accurate artificial boundary condition for the Euler-Bernoulli beam. Numer Algor 93, 1685–1718 (2023). https://doi.org/10.1007/s11075-022-01485-7

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  • DOI: https://doi.org/10.1007/s11075-022-01485-7

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