LUO Han-zhong, LIU Xue-wen, HUANG Xing-chun. Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics[J]. Applied Mathematics and Mechanics, 2011, 32(6): 730-740. doi: 10.3879/j.issn.1000-0887.2011.06.010
Citation: LUO Han-zhong, LIU Xue-wen, HUANG Xing-chun. Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics[J]. Applied Mathematics and Mechanics, 2011, 32(6): 730-740. doi: 10.3879/j.issn.1000-0887.2011.06.010

Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics

doi: 10.3879/j.issn.1000-0887.2011.06.010
  • Received Date: 2010-07-21
  • Rev Recd Date: 2011-04-13
  • Publish Date: 2011-06-15
  • Reproducing kernel collocation method based on strong formulation was introduced for transient dynamics.von Neumann stability and dispersion analysis of reproducing kernel collocation method with central difference temporal discretization was derived to evaluate the stability condition for second order wave problem.The stability analysis algorithm proposed firstly given an approach to predict critical time step for second order wave problem which can greatly save computational time in application.A numerical test was conducted to validate this algorithm.The comparison of numerical critical time step and predicted results shows good agreement.The guidance to choose a proper support size of reproducing kernel shape function is also given.The results by radial basis collocation method are also listed for comparison.
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