October  2010, 14(3): 1029-1054. doi: 10.3934/dcdsb.2010.14.1029

A spectral collocation method for solving initial value problems of first order ordinary differential equations

1. 

Department of Mathematics, Shanghai Normal University, Shanghai 200234, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai E-institute for Computational Science

2. 

Department of Mathematics, Shanghai Normal University, Guilin Road 100, Shanghai, 200234, Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities, China

Received  November 2009 Revised  May 2010 Published  July 2010

We propose a spectral collocation method for solving initial value problems of first order ODEs, based on the Legendre-Gauss-Lobatto interpolation. This method is easy to be implemented and possesses the spectral accuracy. We also develop a multi-step version of this process, which is very available for long-time calculation. Numerical results demonstrate the high accuracy of suggested algorithms and coincide well with the theoretical analysis.
Citation: Ben-Yu Guo, Zhong-Qing Wang. A spectral collocation method for solving initial value problems of first order ordinary differential equations. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1029-1054. doi: 10.3934/dcdsb.2010.14.1029
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