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Volume 33, Issue 1
A Chebyshev-Gauss Spectral Collocation Method for Ordinary Differential Equations

Xi Yang & Zhongqing Wang

DOI: 10.4208/jcm.1405-m4368

J. Comp. Math., 33 (2015), pp. 59-85.

Published online: 2015-02

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  • Abstract

In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.

  • Keywords

Initial value problems of ordinary differential equations, Chebyshev-Gauss spectral collocation method, Spectral accuracy.

  • AMS Subject Headings

65L05, 65L60, 41A10.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rachel0313@126.com (Xi Yang)

zqwang@shnu.edu.cn (Zhongqing Wang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-59, author = {Yang , Xi and Wang , Zhongqing}, title = {A Chebyshev-Gauss Spectral Collocation Method for Ordinary Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {1}, pages = {59--85}, abstract = {

In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1405-m4368}, url = {http://global-sci.org/intro/article_detail/jcm/9827.html} }
TY - JOUR T1 - A Chebyshev-Gauss Spectral Collocation Method for Ordinary Differential Equations AU - Yang , Xi AU - Wang , Zhongqing JO - Journal of Computational Mathematics VL - 1 SP - 59 EP - 85 PY - 2015 DA - 2015/02 SN - 33 DO - http://doi.org/10.4208/jcm.1405-m4368 UR - https://global-sci.org/intro/article_detail/jcm/9827.html KW - Initial value problems of ordinary differential equations, Chebyshev-Gauss spectral collocation method, Spectral accuracy. AB -

In this paper, we introduce an efficient Chebyshev-Gauss spectral collocation method for initial value problems of ordinary differential equations. We first propose a single interval method and analyze its convergence. We then develop a multi-interval method. The suggested algorithms enjoy spectral accuracy and can be implemented in stable and efficient manners. Some numerical comparisons with some popular methods are given to demonstrate the effectiveness of this approach.

Yang , Xi and Wang , Zhongqing. (2015). A Chebyshev-Gauss Spectral Collocation Method for Ordinary Differential Equations. Journal of Computational Mathematics. 33 (1). 59-85. doi:10.4208/jcm.1405-m4368
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