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

Ben-Yu Guo; Zhong-Qing Wang

doi:10.3934/dcdsb.2010.14.1029

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2010, Volume 14, Issue 3: 1029-1054. Doi: 10.3934/dcdsb.2010.14.1029

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

Ben-Yu Guo^1, and
Zhong-Qing Wang^2,

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

Received: October 31, 2009

Revised: April 30, 2010

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 65L60, 65L05, 41A10.

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