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Legendre–Gauss collocation methods for ordinary differential equations

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Abstract

In this paper, we propose two efficient numerical integration processes for initial value problems of ordinary differential equations. The first algorithm is the Legendre–Gauss collocation method, which is easy to be implemented and possesses the spectral accuracy. The second algorithm is a mixture of the collocation method coupled with domain decomposition, which can be regarded as a specific implicit Legendre–Gauss Runge–Kutta method, with the global convergence and the spectral accuracy. Numerical results demonstrate the spectral accuracy of these approaches and coincide well with theoretical analysis.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, 200234, Shanghai, People’s Republic of China

    Ben-yu Guo & Zhong-qing Wang

  2. Division of Computational Science of E-institute of Shanghai Universities, 200234, Shanghai, People’s Republic of China

    Ben-yu Guo & Zhong-qing Wang

  3. Scientific Computing Key Laboratory of Shanghai Universities, 200234, Shanghai, People’s Republic of China

    Ben-yu Guo & Zhong-qing Wang

Authors
  1. Ben-yu Guo
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  2. Zhong-qing Wang
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Correspondence to Ben-yu Guo.

Additional information

Communicated by Zhongying Chen.

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Guo, By., Wang, Zq. Legendre–Gauss collocation methods for ordinary differential equations. Adv Comput Math 30, 249–280 (2009). https://doi.org/10.1007/s10444-008-9067-6

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  • DOI: https://doi.org/10.1007/s10444-008-9067-6

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