# American Institute of Mathematical Sciences

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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