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

YAN Jian-ping; GUO Ben-yu

doi:10.3879/j.issn.1000-0887.2011.12.005

Volume 32 Issue 12

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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

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

doi: 10.3879/j.issn.1000-0887.2011.12.005

YAN Jian-ping^1,2,
GUO Ben-yu^1,3,4

Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China;
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, P. R. China;
Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, P. R. China;
Division of Computational Science of E-Institute of Shanghai Universities, Shanghai 200234, P. R. China

Received Date: 2011-08-17
Rev Recd Date: 2011-09-26
Publish Date: 2011-12-15

Abstract

Abstract

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.
- Laguerre-Gauss collocation method,
- initial value problems,
- second order ODEs

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References(31)

References

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