Applied Mathematics and Mechanics

, Volume 32, Issue 6, pp 777–788

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

  • Han-zhong Luo罗汉中
  • Xue-wen Liu刘学文
  • Xing-chun Huang黄醒春
Article

DOI: 10.1007/s10483-011-1457-6

Cite this article as:
Luo, H., Liu, X. & Huang, X. Appl. Math. Mech.-Engl. Ed. (2011) 32: 777. doi:10.1007/s10483-011-1457-6
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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.

Key words

reproducing kernel collocation method (RKCM)stability analysisdispersion analysistransient dynamics

Chinese Library Classification

O302

2010 Mathematics Subject Classification

65M12

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Han-zhong Luo罗汉中
    • 1
  • Xue-wen Liu刘学文
    • 2
  • Xing-chun Huang黄醒春
    • 1
  1. 1.School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghaiP. R. China
  2. 2.Siemens Industry Software (China) Co., Ltd.ShanghaiP. R. China