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A Legendre–Gauss–Radau spectral collocation method for first order nonlinear delay differential equations

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Abstract

In this paper, we introduce a single-step Legendre–Gauss–Radau spectral collocation method for solving the first order nonlinear delay differential equations with variable delay, and analyze its convergence. We also propose two fast and efficient algorithms for the single-step scheme and apply them to the multiple interval case. Numerical results show that the suggested algorithms enjoy high order accuracy.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Lijun Yi

  2. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Zhongqing Wang

  3. Division of Computational Science, E-Institute of Shanghai Universities, Shanghai, 200234, China

    Lijun Yi & Zhongqing Wang

Authors
  1. Lijun Yi
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  2. Zhongqing Wang
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Correspondence to Zhongqing Wang.

Additional information

Lijun Yi is supported by the NSF of China (Nos. 11226330 and 11301343), the Research Fund for the Doctoral Program of Higher Education of China (No. 20113127120002), the Fund for E-Institute of Shanghai Universities (No. E03004) and the NSF of Shanghai (No. 15ZR1430900). Zhongqing Wang is supported by the NSF of China (Nos. 11171225 and 11571238), the Research Fund for Doctoral Program of Higher Education of China (No. 20133127110006) and the Fund for E-Institute of Shanghai Universities (No. E03004).

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Yi, L., Wang, Z. A Legendre–Gauss–Radau spectral collocation method for first order nonlinear delay differential equations. Calcolo 53, 691–721 (2016). https://doi.org/10.1007/s10092-015-0169-5

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