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Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics

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Abstract

A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to predict the critical time step. A numerical test is conducted to validate the algorithm. The numerical critical time step and the predicted critical time step are in good agreement. The results are compared with those obtained based on the radial basis collocation method, and they are in good agreement. Several important conclusions for choosing a proper support size of the reproducing kernel shape function are given to improve the stability condition.

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Authors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China

    Han-zhong Luo  (罗汉中) & Xing-chun Huang  (黄醒春)

  2. Siemens Industry Software (China) Co., Ltd., 14F, Cloud-9 Office Tower, No. 1018, Changning Road, Shanghai, 200042, P. R. China

    Xue-wen Liu  (刘学文)

Authors
  1. Han-zhong Luo  (罗汉中)
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  2. Xue-wen Liu  (刘学文)
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  3. Xing-chun Huang  (黄醒春)
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Corresponding author

Correspondence to Xing-chun Huang  (黄醒春).

Additional information

Project supported by the Western Transport Technical Project of Ministry of Transport of China (No. 2009318000046)

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Luo, Hz., Liu, Xw. & Huang, Xc. Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics. Appl. Math. Mech.-Engl. Ed. 32, 777–788 (2011). https://doi.org/10.1007/s10483-011-1457-6

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  • DOI: https://doi.org/10.1007/s10483-011-1457-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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