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An adaptive algorithm for the Thomas–Fermi equation

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Abstract

A free boundary value problem is introduced to approximate the original Thomas–Fermi equation. The unknown truncated free boundary is determined iteratively. We transform the free boundary value problem to a nonlinear boundary value problem defined on [0,1]. We present an adaptive algorithm to solve the problem by means of the moving mesh finite element method. Comparison of our numerical results with those obtained by other approaches shows high accuracy of our method.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China

    Shengfeng Zhu

  2. Department of Mathematics, Shaoxing University, Shaoxing, 312000, Zhejiang, People’s Republic of China

    Hancan Zhu

  3. Department of Mathematics, Zhejiang University, Hangzhou, 310027, Zhejiang, People’s Republic of China

    Qingbiao Wu & Yasir Khan

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  1. Shengfeng Zhu
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  2. Hancan Zhu
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  3. Qingbiao Wu
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  4. Yasir Khan
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Correspondence to Shengfeng Zhu.

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Zhu, S., Zhu, H., Wu, Q. et al. An adaptive algorithm for the Thomas–Fermi equation. Numer Algor 59, 359–372 (2012). https://doi.org/10.1007/s11075-011-9494-1

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  • DOI: https://doi.org/10.1007/s11075-011-9494-1

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