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Volume 7, Issue 2
Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations

Lijun Yi & Zhongqing Wang

DOI: 10.4208/nmtma.2014.1309nm

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 149-178.

Published online: 2014-07

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  • Abstract

In this paper, we present and analyze a single interval Legendre-Gauss spectral collocation method for solving the second order nonlinear delay differential equations with variable delays. We also propose a novel algorithm for the single interval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy of the proposed methods.

  • Keywords

Legendre-Gauss spectral collocation method, second order nonlinear delay differential equations, error analysis.

  • AMS Subject Headings

65M70, 65L05, 65L70, 41A10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-149, author = {Lijun Yi and Zhongqing Wang}, title = {Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {2}, pages = {149--178}, abstract = {

In this paper, we present and analyze a single interval Legendre-Gauss spectral collocation method for solving the second order nonlinear delay differential equations with variable delays. We also propose a novel algorithm for the single interval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy of the proposed methods.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1309nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5869.html} }
TY - JOUR T1 - Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations AU - Lijun Yi & Zhongqing Wang JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 149 EP - 178 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1309nm UR - https://global-sci.org/intro/article_detail/nmtma/5869.html KW - Legendre-Gauss spectral collocation method, second order nonlinear delay differential equations, error analysis. AB -

In this paper, we present and analyze a single interval Legendre-Gauss spectral collocation method for solving the second order nonlinear delay differential equations with variable delays. We also propose a novel algorithm for the single interval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy of the proposed methods.

Lijun Yi and Zhongqing Wang. (2014). Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 7 (2). 149-178. doi:10.4208/nmtma.2014.1309nm
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