YAN Jian-ping, GUO Ben-yu. Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1439-1460. doi: 10.3879/j.issn.1000-0887.2011.12.005
Citation: YAN Jian-ping, GUO Ben-yu. Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1439-1460. doi: 10.3879/j.issn.1000-0887.2011.12.005

Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs

doi: 10.3879/j.issn.1000-0887.2011.12.005
  • Received Date: 2011-08-17
  • Rev Recd Date: 2011-09-26
  • Publish Date: 2011-12-15
  • Numerical method for initial value problems of second order ordinary differential equations was investigated. The new collocation method based on the Laguerre-Gauss interpolation was designed, which was very easy to be carried out, especially for nonlinear problems. The convergence was analyzed for two different cases, and the spectral accuracy was proved by using the recent results on the LaguerreGauss interpolation. A multi-step collocation method was also provided, which simplified actual computation and still kept the same spectral accuracy. The numerical results are presented, demonstrating the high accuracy of suggested algorithms.
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