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Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation

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Abstract

A new family of exponentially fitted P-stable one-step linear methods involving several derivatives for the numerical integration of the Schrödinger equation are obtained. Numerical results are reported to show the efficiency and robustness of the new methods specially adapted to the integration of the radial time-independent Schrödinger equation for large energies. Error analysis is carried out and the asymptotic expressions of the local errors for large energies explain the results of the numerical experiments on the resonance problem.

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Acknowledgments

This research was partially supported by National Scientific Foundation of China (NSFC) under Grant Nos. 11571302, 11171155, the foundation of Scientific Research Project of Shandong Universities under Grant No. J14LI04 and the Fundamental Research Fund for the Central Universities (No. KYZ201424). We are grateful to anonymous reviewers for their constructive comments and invaluable suggestions which have helped to improve the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Yanwei Zhang & Yonglei Fang

  2. College of Sciences, Nanjing Agricultural University, Nanjing, 210095, People’s Republic of China

    Xiong You

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  1. Yanwei Zhang
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  2. Xiong You
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  3. Yonglei Fang
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Correspondence to Xiong You or Yonglei Fang.

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Zhang, Y., You, X. & Fang, Y. Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation. J Math Chem 55, 223–237 (2017). https://doi.org/10.1007/s10910-016-0683-y

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