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Multiscale orthonormal method for nonlinear system of BVPs

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Abstract

The aim of this paper is to find numerical solutions of nonlinear boundary value problems (BVPs). First, the nonlinear system is transformed into linear system using the Quasi-Newton’s method, and the convergence of the method is verified. Second, we defined Hilbert space \(W_{(2,2)}\) and constructed a set of multiscale orthonormal basis in \(W_{(2,2)}\). By solving the \(\varepsilon -\)approximation solution of the linear systems, the numerical solution of linear systems is obtained. Furthermore the feasibility and effectiveness of the proposed method are verified by three numerical experiments.

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Funding

This work has been supported by three research projects (XJ-2018-05, ZH22017003200026PWC, 2022WZJD012).

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Authors and Affiliations

  1. Beijing Institute of Technology, Zhuhai Campus, Zhuhai, 519088, Guangdong, China

    Yingchao Zhang, Liangcai Mei & Yingzhen Lin

Authors
  1. Yingchao Zhang
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  2. Liangcai Mei
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  3. Yingzhen Lin
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Contributions

YZ conceived of the study, designed the study and collected the literature. LM proved the convergence of the algorithm. YL reviewed the full text. All authors were involved in writing the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Liangcai Mei.

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The authors declare that no competing interests exist.

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I declare that the papers submitted are the results of research by all of our authors.

Additional information

Communicated by Zhaosheng Feng.

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Zhang, Y., Mei, L. & Lin, Y. Multiscale orthonormal method for nonlinear system of BVPs. Comp. Appl. Math. 42, 39 (2023). https://doi.org/10.1007/s40314-022-02170-0

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