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A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

Part of: Approximations and expansions Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  17 November 2016

Zhong-Qing Wang  and
Jun Mu
Zhong-Qing Wang*
Affiliation:
School of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China
Jun Mu*
Affiliation:
School of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China
*
*Corresponding author. Email addresses:zqwang@usst.edu.cn (Z.-Q. Wang), mujun06@163.com (J. Mu)
*Corresponding author. Email addresses:zqwang@usst.edu.cn (Z.-Q. Wang), mujun06@163.com (J. Mu)
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Abstract

We introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain the hp-version bound on the numerical error of the multiple interval collocation method under H 1-norm. Numerical experiments confirm the theoretical expectations.

Keywords

Multiple interval Chebyshev-Gauss-Lobatto spectral collocation methodnonlinear ordinary differential equationserror analysis

MSC classification

Secondary: 65L05: Initial value problems 65L60: Finite elements, Rayleigh-Ritz, Galerkin and collocation methods 41A10: Approximation by polynomials 65L70: Error bounds

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 4 , November 2016 , pp. 619 - 639
Copyright
Copyright © Global-Science Press 2016 

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